{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "3f805402-f769-464e-8005-b5871f10e857",
   "metadata": {},
   "source": [
    "# Overview \n",
    "1. order of differential - take the highest order\n",
    "2. number of independent variable\n",
    "   > more than one - pde partial differential equation <br>\n",
    "   > only one - ode ordinary differential equation <br>\n",
    "3. coefficient - for simplicity we only look at constant coefficient ode|pde\n",
    "4. linarity\n",
    "   > for first-order ode|pde it's intrinsically linear\n",
    "   > for higher-order ode|pde, linear means no high power or cross differential terms\n",
    "\n",
    "<hr>\n",
    "\n",
    "有固定解法的<font color=red><b>ode|pde</b></font>一般都是<font color=maroon><b>线性(常系数)k阶常微分｜偏微分方程｜方程组</b></font> <br>\n",
    "\n",
    "对于一阶常微分方程，我们不讨论是否是否是常系数，也不讨论线性，也就是说，<font color=maroon><b>一阶常微分方程</b></font>，固定的有闭式解方法，同样，数值解我们也有R-K方法进行计算机计算<br>\n",
    "对于二阶常微分方程，我们在求闭式解时需要限定线性的条件，也就是说，<font color=maroon><b>二阶线性常系数常微分方程</b></font>，我们可以采取叠加原理计算闭式解，同样，数值解我们也有R-K方法进行计算机计算<br>\n",
    "对于更复杂的高阶非线性常微分方程，我们只能求助于数值解，这时需要我们使用python进行协助计算"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0be06023-a86e-4375-8d02-a998655eaaf4",
   "metadata": {},
   "source": [
    "# Directional Derivative & Partial Derivative\n",
    "Inspecting derivatives near $P_0(0,0)$ of this following function:\n",
    "$$\n",
    "    f(x)=\\sqrt{x^2+y^2}\n",
    "$$\n",
    "According to differentiable conditions, we got\n",
    "$$\n",
    "    \\frac{\\partial{f{(P_0)}}}{\\partial(\\vec l)} = \\mathop{\\lim}\\limits_{\\rho \\to 0} {\\frac{\\sqrt{x^2+y^2}-0}{\\sqrt{{(x-0)}^2+{(y-0)}^2}}}=1\n",
    "$$\n",
    "Where $\\rho$ stands for reminder of first derivatives. <br>\n",
    "And $\\vec l$ is any direction vector that approaches point $P_0(0,0)$ <br>\n",
    "from this derivation we know that directional derivatives near $P_0(0,0)$ exists in either direction, whilst\n",
    "$$\n",
    "\\left\\{\n",
    "\\begin{array}{ll}\n",
    "\\mathop{\\lim}\\limits_{x \\to 0} \\frac{\\sqrt{x^2}-0}{x} \\\\\n",
    "\\mathop{\\lim}\\limits_{y \\to 0} \\frac{\\sqrt{y^2}-0}{x}\n",
    "\\end{array}\n",
    "\\right .\n",
    "$$\n",
    "both not exists, then we could conclude that $f(x)$ is not differentialbe near point $P_0(0,0)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "fab3e5a9-dce8-4390-99ff-4886e15fc089",
   "metadata": {},
   "outputs": [
    {
     "data": {
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xsZFMJnObGFWjumqqcnjkZoyhUqlQLpdjcYuJeRMQi1nMG4YxphaNVUWlKiD5fJ5Dhw6hlGLnzp04joO1lnnz5mGMYXBwkN7eXrq7uzl//jxKqVrU1tDQQDqdHvOYwyM3+G4xidYarfVtBSXV9OTo7WJiYh4tYjGLeehUI6PhaUUpZU1Yrl27xqlTp5g3bx6LFy9GCEEQBLXtpZTU19dTX18PRKI4MDBAb28vHR0dnD17FsdxkFKitaZUKpFMJu+YlhxdKVltB6jeP3rNLRa3mJhHC1EoFMZfXR/GeL90Y2Imw+gij6ooHD9+HKUU5XKZnp4e1q5dy7Rp00ZsY62dkIBorRkYGODs2bMEQYDv+3ieV4vcGhsbSSaTEz7fqvhWj18Vt2rkVk1LxsTEjE2xWHzgx4gjs5iHRjUa01rftibl+z7d3d00NDSwa9cuEonElI9TTTnmcjkSiQTz5s2jv7+f3t5erl+/Xlufq663NTY2jnu88SK3mzdvcvXqVTZs2BCLW0zMI0AsZjEPnOFpu9HVitZaLl26xK1bt2hoaGDTpk33LX03vGS/qamJpqYmAMIwpK+vj76+Pq5evcqJEydIp9Mj1tw8zxt3n1XxstbW/huGYS0VOpY7SSxuMTEPlljMYh4o4/WOAVQqFY4ePUqhUKClpYVEInHf16HG6lFzHIdp06bV0phBENDX10dvby+XLl0in8+TyWRGiJvrumPuf7zIrZrerD7nWNxiYh4ssZjFPDDu1DvW1dXF0aNHaWxsZOfOnZw/f77WF3a/mKgwuq7L9OnTmT59OhClPKvidv78eYrFItlsdoS43emYo8Wtml6tRm5Vw+SquFWrJWNiYqZOLGYx951q2i0MQ2BkNGaM4dy5c1y+fJkVK1Ywa9asCVcGji4AUXI3Fg9jNt5xm8nieR4zZsxgxowZQBRBVsXt7NmzlMtlkskkYRjW1vmUUmPuq5qSHH4+VXHzfb/23KviNrxaMiYmZuLEYhZzXxlecg8j+7qKxSJHjhwhDEN27NhBNputbSeEmHRk5jj/AynOUfZ/H2sX3Xb//RKERCJBS0sLLS0tAJTLZa5cucLNmzc5ffo0lUqFurq6WtRWX19/T+ImpbytoCQWt5iYOxOLWcx9oXpRvnTpEvX19bfZTd28eZNjx47R1tbG8uXLb7vYT/ZiLTiF6/x3wvBJEt7HqVT+EEvLmOd1v0kmkzQ1NdHX18fWrVsplUr09vbS29tLe3s7QRDUxK2xsZG6urpx18jGE7cDBw7Q3NzMzJkz43E3MTETIBazmHtmeJHH1atXUUqRy+WAkZZUq1evprW1dcx9TDYy89wvEYZP4ahXCPVmEu4vUA6+CNSN2OfDIJVKkUqlmDlzJtbaEeJ27do1tNbU19fXxC2Xy91V3Kr/VUrVxuEMdyeJxS0mZiSxmMXcE6N7x6pOHgCDg4McPnwYx3HYtWsXqVRq3P1M5mIsuIES+7BkCMMnceQetF1Kwvk4lfDzwHd7xh5EZHbHcxOCdDpNOp1m1qxZWGspFos1cbt69SrGGBoaGmp9brlc7rbnP7pBe/hzicUtJuZ2YjGLmRLj9Y5VI6yrV6+OsKS6Wyn6ZCIzV/0XrE0iCIBeQr0DJQ8iKJNQv0pF/w6g7jo+5l6ZyL6FEGQyGTKZDLNnz8ZaSz6frxWUXL58GaAmbA0NDSPWEkfvCxghbsMHlcZTuGPeysRiFjNp7tQ7Zq3lypUrVCoVNmzYUOvluhsTv9j2o8TrYOqwsgdsAskttF6HFOdR4tt48tP45pO183mUEEKQy+XI5XLMmTMHay2Dg4P09fXR09PDhQsXasLveR719fWk0+m7jrsZPcttrCnc1TaAeCJAzJuRWMxiJkU1xTVW71hfXx/9/f2kUil27tw5KUuqiUZRrvgbpDiOYQHoaSA7sLYeyS2MWYAUHbjir7CiDiF+YErP8WEihKCuro66ujrmzp1bmwhw/PhxBgcH2bt3L47jjLDeSqVSkxa3eAp3zJudWMxiJsTw3rHqjLDRllTnzp0jlUoxZ86cSXsr3knMvnuRruDKP0HrrShxFCOKWD0bIW5gqUPSiTEzECJJQnyO5voyN7v+n3t96g+V6kSAZDJJW1sbLS0tt00EcF33NnEbizuJ26uvvsrChQtpbGyMp3DHvCmIxSzmrhhjCMPwrpZUW7Zs4eLFi1M6xkQiM1f8DVgHxUG0WY8UFxDiNMYsR8qbWJtE0oWxzWhWMWva71GpJIDlUzqnRwEpZa1YZMGCBWit6e/vp6+vj/b2dk6fPk0ikRghbuNNBBgublrrmnANn8I91ribWNxiHgdiMYsZl+ENvcOr66p0dXVx5MgRmpqa2LlzJ67rTrno4u7bGTz5Jxg7A0EKxR602YwQHSixH202IUQXIJG2B2vryZfWs3DWpymzBM07J/8C3OV83whGmyZrrWumycMnAgyfwj1elFytPq3uN57CHfM4E4tZzJiMtqQaLmTGGM6ePcuVK1dGWFJVH/cgxEzxf7E2E62N2WkYVqLEPrTZiCGJw0uEdhcwWPsnkPQPbKah7ico2v8PI/7JpM/rUUcpRXNzM83NzcB3JwJU2wDGmwgw1msdT+GOeZyJxSzmNob3jg03zYXIkurw4cNorW+zpIIHJ2au/b9Yq7EkkAxgyaLNGpQ4grYrCNmMw/OEPIXAQdCJFC5KBoT6GdL8GEXxtxi5a9LnNh4Puux/KgJxp4kAFy9epFAokMlkCIKA/v5+MpnMpCcCxFO4Yx5FYjGLqVG9UHV3d3PkyBGefPLJSVlSAbU1mMlyRzELv43V36FSWYGX8FFiAEggUGizHCXOY+xcQr4Hh+fR7MLSiuQK2mYQ9BDap0jZH6XE/8LI8Y2J32yMNxHgxIkTXL9+nfPnz5PL5Ub0uTnO2JeF8cStOsttPHGLx93EPAxiMYsBbu8dq16cYOKWVHD/IzPf9yl1fwEl2qjP7qG7ezmO65JJXsYwF9dVaOYjuQm2kZDvxeElNOsIwjaUvAE2i6QdzTZS+scoif+JEasnfY5vBqoTAU6fPs3q1atJJBL09vbS19dXmwiQy+Vqwna3iQDjidvx48dpbm5m+vTp8RTumIdCLGYxt/WOVYsBYHKWVHB/xay3t5cLZ/8/tq16AS02YdnBjKZXKPobqQSz8Zwz9PbMwnEVrpMl4Q4ipU8o3oayr+PINsqVVhLuAFY0ILmEtmtIBj9J2fnvGLls0uf5ZqGaxkwkErS2ttZ+oJTL5Zr11uiJAFXT5ImIW6VSqR0jnsId8zCIxewtTDWtWK1WHG5JVTUNnowlFUxtlEt1u6qYDe9be2rT10C+DcfuQ9v5hOJp0u5LaHc1VmykueEg5WAhQWAZ9AWCIp5zKhIt9zQJt4hlKcLcxIpmpD2FYSmJ4Kcpu/8FK28fHfMoMNU1s8kw1v6r/W1tbW0AI0yTb9y4QRiGE5oIUD3/4RWT8RTumAdJLGZvUe5kSWWMwVrLuXPn2LhxY61SbiJIKWv7nAxVMfN9n6NHj5LP59mxJUvW68CaBJqNSM6C8Ql5CmX3Y2nFiM2knAMknPlY0YIxA+gQlL1Iz8AcsokbaA7h62UkEoMoORtlj6HFSpLBz1F2/xgr507pfB9nJho9T3UiwFhiHE/hjnmQxGL2FqQajY1nSXXo0CEAduzYMW4D7njcS5oxDENeffVV6urq2LlzJyn9r7AmhxAGaXuH7Kq6kPYyWmxC2tNIew4tNqPMMQwNSDEd5Q4Cc2nKXWawNAfH7SfhHKW3ZzGe24WULWRTBwjFGhL2o1S8P8TKWZM+58eZqUR+Y00EKBQKtWrJK1euYK2loaGh1qd2p+PEU7hj7iexmL2FGN07NtqS6uLFi5w/f5758+dz/vx5PM+b9DGmImbWWm7evEmpVGL58uXMmzcPac8igktYEmD6sKQRFDG2AWErSC5iWIq0N1DmAFpuQNrzCC5hWIiwAwS6jax3GemsQpKjpfEUZb0JrQcYKM4l4x2gv7gA6fwUvfq3qGtYPmnxfpC8EWnGyW6fzWbJZrMjJgJUC0ouXrzI5cuXR7iTZDKZexK3eAp3zHjEYvYWoXpRqK5nDV+XqFQqHDlyhGKxyNatW0mlUpw/f74WuU2GyYqZ7/scOXKEgYEBEokE8+fPj86v/N9A3wTqsGI6wlzHkkFgwSos05H2CoZZkSNIuJtQbUXamyh7HC1WIeim7LdQ555Bs5BQrCUpXidM7CCZ8LFmI425gxQqC8iFv8qBvf8S4bTR1NQ0osF4PN7o8TKP2v6HTwRob29n0aJFeJ5Hb28v3d3dtYkAw8VtvIkA1f2NJ25dXV309vaycOHCeNxNDBCL2Zue4ReAsdKKwy2pdu3aheM4tchtqunCiRaA9Pb2cujQIRoaGli9ejUnT56M7tCXkMH/warlCHMB9HmMXIzQV7FSYpmOMEWsaETaDgzTMGIVrt5NILYCSZTeh9GrgUE0c1D2QtSLJrfhhK+h5TaECDBsJusdJJ1YwNs2/m9uln6Frh5RazDOZrMj3DPG68F63HjQBSbVgqLqRIB58+bVJgL09vbS2dnJuXPnJjwRAEaKW7Xpu7rOGg8qjXlzfDNjxuRuRR7jWVJVo7GpVCUOnzR9p/OqpjSXLl3K3Llz6evrq22n/D8D6pDBa2i1HSnakXofAZtQ5hbSXsCIxQgziBUekgEMOUKxAdfsJRTr0XI1aWcf/cEahJUYZiPtNYxtIVS7cMLX0XIDQhSH1tyOgKgwM/UfaV78Waxciu/7tWKH4T1YTU1NI9oXHlcetJiN3n91IkB9fT3z58/HGFMzTe7o6ODMmTN4njfCV3K8VpCqWMZTuGOqxGL2JsUYQ3d3N8lksmYAXKVqSWWMGdeSCqYemd1pu2pasVAosHXrVurr60dup6+hSn+EdnciZBoVfAftPIEQSbzwRUL1JAgPZQ5FYmQLWNuPEC5Yl1BsRJmjaLGEYrCB+sR+jN2BQGCYhTQ3saZMqHagwv0YuRwhetFyHcqcxuoTJEr/jkrqP+F5LbS0RP9gZJl6d3c3YRhy8OBBGhsbaWpqIpvN3tey8gd10X0YIjyRyE9KWYvIhk8E6O3tHTERYLi4Vdc0R6fAh4+6qR6/+rh4Cvdbg1jM3mQM987bt28fGzdupKGhoXZ/1ZJq5syZLFu2bMwG2OHR22S5k5j19PRw+PBhGhoaai77o7dT5c9jnC1DQrMWo7ajwt1osZFQbsUJv0OodqLFCpzgZUJnJwgHqa9jZRvC+GhWo8wZlJhGb3EDzem9aLUBcNCiDWm6kMEltLMVpY9i5FykvYEWy5DmMjI8TqLwESrpL2LVd91Ohpep9/T0cPLkSaZPnz6ikq96cb5bscPdeBjrcQ87MrsboycChGFYE7fr169z8uRJUqkUjY2NtfaR8RgubmNN4R4ubvEU7jcHsZi9iRgrrVj9wmutOXnyJB0dHaxZs6YWbYzHRNKFYzGWmFlruXDhAhcuXKilFcfqQfJUJ9L/ByxtGLkWoS+DmIVRW5HhSTTzCNVTOOEeQrmaUO3ECV5Eqx0YORelz2HkQgQBRizB4SKeKhKqp1D6dYxcghBJjJyBNH2o8BihWoMyF6P1N30eIxcg7C1keI5k4ScpZ/4Mq2aO+TyFEMyePbtWyVddD+ru7ub8+fMopWrC1tTURDKZfKQulI+amI3GcZxxJwJ0d3dTqVR4/fXXR6y53c00GeIp3G9WYjF7kzBW71i1GGO4JdXOnTvvakkFU3fyGG00XK2ULJVKI9KKYx1v4Yy/xspWhC5gTWYo0hpEmAxGLkXqG1htCOU2lDmKYTahegYnfBmtVqHlclR4DKOWACGBaUPaDqQ+Tyi345hDWNEGIo0VTVjr4gR70M5WpGnHihZUeBytVoJMInQXqcH3Ucr9D6yafdfXa3SxQ3VC9M2bNzlz5kwtZVb9N9lp3PeLRyXNOFmGTwTwPI+BgQFaW1trEwGOHTtWK9ip+krei7j19fXV3rNY3B59YjF7zLlT75gQglu3bnHt2rVJWVJV93OvkVk1rdjY2Mj69evHvbAAKNrJJS6DnQaEYAFcwBLtLsTQiLAhwvaj5SqkuYLQfhR5hfuwopVQrcMJj2DkfIS1VMIGUgic8AihWo8yZ0FUgHqsyGHkEhz/BUL3SYTtxahFqPAA2lmHFS7C5kn3v5Ni3f/GOvMn/DqMNSF6rDljw9sARr8+D3rN7FGPzO6EMQal1JgTAXp7ezl//jzFYrFmmtzY2Eh9ff1dJwLAd8Xtxo0bI4pQxpsIEIvbo0EsZo8xo3vHhn8hq42mN27cmLQlFdzbKBdjDOfPn+fChQssW7aMOXPm3PULn/T/lNDpAd2IlTMQ+hyW2Vg1HRFewtIKIgn0ARmEKWCYiWQAqS+h1UaUPo3S59BqPVIfR9CAsAJLDis8nOB1QmcL0l5H0AW2ESuShM5GHP9bhO7TCFtEy3U4/h5CZxOWerRIke5/B8X6/4t1lkz6NYHbh2hW54z19PSMeeGdyms/WR602DyM0v/hVCcCzJgxA4iyAtWCnTNnzoyYCFAVtzuZJltraw3a8RTuR59YzB5DhveOVX8Bj7akOnz4MADLli2btJDB1G2ptNbk83l832fbtm3U1dVNYKMrOGYPfaVWssnzGDsTK5chgyPR32oxMjiOpgUrpyHtdSyNCKExZBAihTSX0HIZ0lxDhQfRzgakPoMjDVAHwsWolbjhq4RqO9hehOkC2QA2Teg8gVP5FqH7NoSoROtx/stodwNWeBixlHTvD1Bq+BuMu2rSr8toRs8ZG37hPXXqFJVKhfPnzzM4OHhHQ9+p8LimGYczEbG800SAkydP4vv+HScCDK+YHP0du9MU7ljc3hhiMXvMGF3kMfxLNrx/a/HixXR0dEz5AjiVNbPu7m5Onz4NwM6dOyfcYKwK/wWhr5N2BcZZjwiPghnEuBsR4REI8xi1CqlPYHUBo+YhwwtYWYcQWbDlyBHEXMaI2QhSOP6rFMwGrL2K0Dcwsg0BaLkJJ3iZwNmBlB7CdGCFRugUofsMjv8S2tuOIE/ofg9O8BraWQ44aLWKVN+PUKr/L8D9ddsffuG11rJ7924aGhooFApcu3YNY0zN0LfaBnCvlZKPc5pxrMjsbgyfCFBdG7vTRACt9bjHGMs0+U5TuIebJsfi9mCIxewxohqNVb9kw78Uoy2p6uvr6ezsnHK6ajJrZtZazp8/z8WLF5k5cya9vb0Td8oILyFLXyFUqxHiKMI/hHHXI/VFZOUA2tsQ/e0fIlDrcbiIDI6hnbVIcwlMPjIJtoNYmpG6HSNboqZp/Ro9wVrSKYsKLmLUAiAkVNtx/VcJ3a1YEfWeIQzogND7HlTldYy3DmE7Cd2dqOBAJKC2Ey2Xkez/CAnxa0DjlF7bu1G9SE6bNo3m5uaaoW/1wnvp0iWEECOKSe5kC3Wn4zwIqp+bBznKpbpmNlWEELdNBCgWi7U1t2vXrhEEAZcvX6ZUKo2YCDDe/sYSt7tN4Y7F7f4Ri9ljwPBffHeypGpubmbDhg01IZlqEQdMPDIbXq24bdu2WrpsosjCn4Bowglep1BeQCYjUJXdGG8rkEGVX8V420CmcYNXCd0dSNmB8l9FOzsQ3ESGp9BqJcL0Y0khTTeWBkp2E42JfRi7C6MSyOA8xl2MsD6huwsneJVQbcDKmWC6EbaMCK6jve2o4AhGLUKGl9DORqQ+ixVNSH0O4yyhIfiPTE+9G9g5pdf3bgx/34Yb+s6ZM2dcW6jRbQAT2feDPPdHLTK7E0IIMpkMmUymNhFg9+7d1NXVMTg4OGIiQPV1vlN0PFFxs9aSSCRqvW7xLLepE4vZI85ULamqj32QkVl3d3fN17Eqol1dXRO/WAZncPL/L9rbgVVJmlJHsWzHuGlk5SDGXYN11iArBwndtaDW4Aa7CZxNoJI4le8Qek9ghIfy96HdzUOOIBUQeQQOPeU1TJOvEzob0M4yVHAK4yxBmAKh8ySO/xpaLcWq6UA/wvrI8CzaXY8MzmPldFRwZCgSvI6VrSh/LwHrmJ/7G5x8K2H2R6f0Gk+V0bZQWutaG8CNGzc4ffo0yWRyROQ23DD5QYvNwxCzB11gUt13S0sLjY2NIyYCVFsBhBCTmggwlrgdPnyY6dOn09bWhhDiNneSWNwmTixmjzDGGG7evEk2m8XzvElZUsG9idmdIrPhacXly5cze/bsEe0AEz2mGvwCxt2M8g8SqlX0FxcwzT2HdeZj3OWI8ArWmYlxV6LCi2hmEqr1OMFxtFpO6G7D8V8m9LahndXR3+5OhHAQpgNhMyhCQmcnjr8H7SxFq1Wo4CRGLUTaHkJvJ8o/iLEVrJoBoogwClU5hHbXIU0HRi7CqbxC4O1C2h60Wk3Kf5lBs5a64l8hbD9B7l9N6XW+Hwxvzl64cOGI5uLLly9z/PjxEYbJ1ajtcRaz+x2ZjcXoApDqRIC5c+dijKmJ21QnAlQjM8/zau0A8RTuqROL2SNINa0YBAGHDx9mw4YNIxps29vbOX78+B0tqWDqjc8wfmRWqVQ4fPgw5XJ5zGrFCac2/WOo0tcwahnGXYsMrmNxMGoWUg9gZQ4rm6IGapFC22kY3Yt0GjDOMmR4Leorc5+IojK1IhKt8ovoxE6smIkyF8DWI/QgobsN5R/CqDa0sxoZnMY6c5BhO9rZiApPYG2AVW1Y6WFRqMputLcNYQcI3Y24pW8SJp9B2AJlsYMZyRcJ7TM4xf8LeoCg/uNwHy/gUxWD4c3F8N3+q56eHs6ePUupVALg/Pnzdy1RnwpvhsiseozxxGOiEwFGmyaPPufh69+jI7c7DSqNxe12YjF7xDDGEIbhG2pJBWMLYXd3N4cPH6a5uZmNGzeOWeQx0ZJ+p/8zGGc1Qt/E0gSiAUU/GEnUNG2jvjLTQSV0KOSLeKpAoA3K8fDcHK7sRyqNURtR+hRGtBF6z+BUXkK7awiZT0KeAbEYYfrQ7jpUcAZryxh3OdK/gHVmIMOLaGcFMrwURYNqJogsxlmOU36ZMLEdYSqEySdxSt+IBM0McKuwiRl2NzqxCbf4HMIM4jd+CsT4zeET5X6ua43uv+rt7eXgwYNUKhVOnDhBGIa1Ssm7FTpMhDdjZHY3xpsI0Nvbe9tEgKrApVKpcY9RLRapMlzcgiCoPWa4uFWrJd+qxGL2iDBe71g1VTgVS6r7tWZmreXcuXNcunTptrTiaCYiZqL8GiI4jxV1WFkH1mBFCk9dAzsdq6Yhg7NotZBCKYdjTpNJL8Vxm8iEFyjpNgJfE5gBtDU4TgGl5pF0OpHGJ0x8D6qyB2XbGPDnkvSuYdVshO1FO0uR+irKP452VyPCa1g5DRWcRKtlUXoyuIqV00GmCd31OKXd6OQmhPEJE8/glF5Dq3V4socw8SQqOIpRs3GK/4AwBSpNvwkyN6XX/WGQSCSQUrJy5cpaFV91LWh0oUNTU9OkDZPfTJHZVI8xfCIAMGIiwPXr1zl16hSJRKIWNWez2Tvam91J3EZP4R5dLflWIRazR4DRllTDy3WllHR0dHDjxg3mz5/PokWLJvVr8V7XzMrlMkeOHKFSqbB9+3ZyuTtfpCcSDarez2BlIxgNIonQ10HMoOhPJxucxrKIQCyF4h50MJtkdgNuuJ/QLMO6y8iYo5j0IoyYD/4lKqaJwM9TKibxnDKuc5qyWkfSnCbl9GGcNVExh5qGMF0YORtpOlHlPWhvK0J3YuScqNDDXQ0kELobTAVkHWFiM6pyDOMuiiK0xC6cylGwDcjgCtpZg9A3gAxO8R8Rpp9K029jndY7vg5vFKMrJatVfFXD5NGFDsMvzHcboAnfnbbwOEdm1QKN+5V+HW8iwNGjR+ns7OTy5cuk0+kRa253mnI+GXGrVkq+2cUtFrM3mOG9Y8Nz5hBZHpXLZdrb26dsSVVNV04WKSX5fJ7z588zbdq0cdOKo7nbOp0sPIeggrUCYfrB5LBqAcI/iitShO56VGUfxVId1l1HQ/IU1jjoxA5UeS9Gt6K9DajKfoSchfEWkw7PYL02DAodlgmDABmepbPcRsa7hSnux3fWktDtIDJI3YkR0xBOEqf0EkFqF9IMYNQSVOUA2l2HVR5S9yD0LZCNaG8dMrgAsh4R3KQiV6DEBaAB5Z9Cu0uBImBQ5ddI3vqXlJt/F5tYMaXX/0E2Hd9p32MVOlQrJcdKlzU1Nd0WUTzohml48JHZgxbk6kQAIQRr1qwhkUjcVrSTyWRGrLndydt0uLgNn+UWBAHXrl1Da83s2bPf1LPcYjF7g7hb71hvb2/Nkmrp0qVTtqSaSmRWrdQqFousWrXqtpL/ux1z3MjMWlT/58D6CCRWzkIEZxFmAOuuJ+nsQRdP0V1czLTsDZRqx3jbEP4JZOU0obsJJziF9c+gE5tR/jFkUBxa/zqNUg1Ipx5XFYF5THOu01uYgVR5EpXddJZXkE704ygXV7WDO4PQW4db/A5h6imEKaGddTiVfYSJ9VGq0eSRYQdG+hhnEcJ0Ighw9WXywXTSUgH1KP8oxl2GoQkhFCLoIH3zfZSm/yEm/eSk34MHzUTfz7EMk6vpsmvXrnHy5EnS6fSIyO1hiNmDjsyq35uHtS43umgnCAJ6e3vp6+u7bSJAVeDuZJoM3x1UWiwWa/Pf3sxTuGMxewO4U+/YcEuqJUuWcOvWrSl/oaZSAFIulzl8+DCVSoU5c+Ywe/adR5+M5k5iJgf/AmyIJYfQnQjbg3WXI4ILiNJB+kvzySW6mJG5AokNYG4gS4fQyTXIoB2nfIQwuQ4VXkMVDxCmNqKCi6jKkaiMPryAoIBx5iDMAFq0kHGukUguRdBAqzhEXmxDh934lQpKXESLJlxnI5nCkKDhE3rbcIqvESbWIGQdRiaR/hWs8TFOG1aWsGE3WecK2FUYkURIgfTPYtU0jGwG6WGBdPt7KU//HGHdj0zqdXyQ3EtxyfB02aJFi2qGycPHsKTTaay1dHd339Gp/l54WJHZgxbM8UTZdd0RRTu+79fE7dy5c5OaCFB1S3mzT+GOxewhY4zB9/0xo7GxZn91d3ffUxHHZLatOolMmzaNVCp1x7TGnY5ZXW8Y8UUwZeTg/wBjEeYaxlmA1DeRxdcpqfX4JUNT8jSktiJkAVE5ikmsBDeLrJzCOIvBTeNUjqHd5Qg3g1PcExVm0IlTfoUwuQOh21H+SbS7EmF78U0dqfAGRrUQJreRLb5MmHkaYUvooB+rBykFmlvBGprNS+TtOjynhPF24FX2ob0lINNoZzEqvIgMrkbl/XI6gamQDM5iVBtWNmJwEaYQFZMkliNsQJjYRbLj5/Arp/Gn/RqIN76U+n5GTmMZJre3t3Px4kVOnz5NpVIZ4XdYX19/XwTiYUVmD0MwJ7Iu53keLS0ttQrm4cbU1dd5vIkAWusR62/DI7c7TeH+xCc+wT/7Z/+MH/iBH7ivz/tBEYvZQ2J471j1izj8i9LZ2cnRo0fHtKR60GJmjOHcuXNcvnyZFStWMHv2bI4fPz7lETBw+wVT9X0JEXZjVQtIUOU9hInN+EbgBq9ivM3kiy6NzmlsYhnWXYjwr2GdFnDmIsObaNkciWBwBaNmYryVqPIRtLcS7a3GKbxAmHoCI5Oo0l4CtQFMaWidrAsrmwhTb8MpPk+YfBLlNIPsp86pYJMOvt1F1t9Hf2URoniFfrGMBn0O48xCOZGgyfAqMriGpJ5K2EhGWkTYi6AH48wB6WJlI07pNcLEDoQtEKT+CW7/f0dWTlFu+39B3b3S8UGn6h7UvhOJBE1NTVy9epWdO3dSKpVuM/MdXuSQy+WmdC4PIzJ70I739xL9jZ4IUCqVahFydSJAfX09DQ0NlMtlMpnMuPsaXnA2XNz27dvH9u3bp/DM3hhiMXsI3Ksl1VSLOCayZlZNK/q+P6JacaL9YmMdE0alsnQXovhNrGpClg9jvLVoZxUi/xLFylLq6jaT1pcp2ga0moeju7GyPirb12UQCiuSUXUhCisbo+IRmUV7S5H+RYw7hzC5bUhENqMTa0gWXyNvV2FFBmwYbUOaMPW9OMUX0MktWNkEph9hyiRsJyb9BI2Vw2hnISbooqBX4lXOUSqmcWQXRrWScnoQdpCULGHlEiABNkCVD6OTaxAYwuRTOMUX0antqPAmOrEJEVwnfeX7Kc36r1hv4aRf2/vFw/BmrH4ORpv5DjdMvnz5MsCINoCJGiY/jGrGB71eNnzyxb1SfZ2rEwGGi1t/fz/9/f309PTQ0NBAU1PThEyTi8XiHUXwUSMWswdMEAQUCgU8z7vtl96DtqS625pZZ2cnR44cYcaMGWzatGlEzv1eJk3DyAum6v7dqHdLzcIk1iKKu+ktL0Cq1TSnb2BFA9adjytvgMmCGnqNrIMwXZERMCDDmxhnNgLADoJJRYUkzgxk2IOVDYSJyOlDe8uouFtpNq9g7BMI0Yg1XQh8CLoIU0/jlF5Be8tB1g9NlS4g/TPoxDpk5RzCa6E+vIZ21+H5lwi0h6sv0JtvwxV5IEEyf4QwsQKlHLS3BqfwGmF6B8IMEqSfxikfxLjzkf4ZrLsIY31SV/9/VFp+C519ZtKv7/3gYYxnGWv/ow2TrbU114yuri7Onz8/wjB5+JTn0TysyOxBUl3Lut/PQwhBOp0mnU4zc+ZMyuUyzc3NOI5DX1/fbSOFqqbJw59v9YfH3VpxpkJ3dzdPPvkkzz33HPPmzbvt/ne961285z3v4f3vf/+k9huL2QOi2jvW09PD/v37eeaZZ0Z8aCdqSfUg0ozD04orV65k1qxZtz1GCDGliHC0mInKaUT5ENZZiCzvo2TmMlBYRnPqOjK5ACuWRm73IodEY5FYUY+onMd6S7CqBVk+ivbWYFUbqnIcnViNkM1I/zLaXRAJmiiBrSCsQbvrUZXTGKbTVdnADPagkxuwsgX0LRAppH+dILkLp3wA47SBasZIhTQuqnQIndyADK5j5CxUeT86uQlPd4KYz3R1iqJYSbnYS17Poa70Oj3BCjxXIZ0dZAr7MemNKP86obcBGV4HssjKSYwzC+PMInHr1wnKxwmm/fxdX8sHwaPQAyaEuM0Sqlop2d7ezunTp0kkErWobXjv1cNYM3sYkdnDsKMyxpBOp5kxY0atl3B0hDy8Ub5UKrFw4UIKhcKYP7Dvha6uLt773vfWovLRfOUrX+Gb3/wm73nPeya971jMHgDV/o7qF2L4r8ipWFLdTzGrphWDIBg3GqxuO5XIrPrlrC1ud/0OIriOpZ7eygrSnKApMxOZXBf1cOEAFoHF1/Vkg3Mgl2G9pcjiPkxiLSaxFlV8jdBdH0U/xd2EiU1od1GU2kusBtGEDK9j1QyEKWPcxUj/KglhCdNvQ5V2Y9wFWNWC0LewKovyLxEmNqH8E2ADUDOw0sE6ClV8FZ3ajtA9GHclTv5FwvQTCJtHe2vJFF+jZFeSy2TR4imaCy+RF+swlU5uBitp1CcJxUyS8igmtRyJD9Ygwh6kvYFOrMAZ/Dqyco5K62dAjXwfHmQq8GGmGSfDaNeMamPxWL1X1QnPD4qHFZk9LDEb/mN5rAh5eKP8Bz7wAW7dukVDQwN/93d/RzabZdWqVfflXD/wgQ/wnve8hz179tx2X09PD7/8y7/M0qVLp7TvN7606k1EtcjD9/1aE7TjOGitaymV1157jUKhwM6dO+8qZHB/xayzs5NXXnmFdDp9RyG7l+OOKADJfwPhXyKQC/BLV/DsVWR2G46SEHRhRRos0bqVfwmBT+CsRJYPQTiISW9Hlg5B2I9OP4njH0UEfYSpJ3AqByEYQCc24ZQOIXQJo+Yi/GuABBui5QwEAulfRKe2I4ObyOAGVrWCLmHVNJxKVPmIMdG21oDIYLxIwKxqBBsSprbj5L+JJY1AU/Z20uQcwaKQpoDOPEOWc2SyzczIDaAT6xD4FIIsemAfg/195CtZApNEy9k4+e9gRRpZOUPy2k8jy2cm/VpPlTcqzThZqo3FixcvZuvWrTz55JMsWLCg5nZx4MAB9u3bx/nz5+np6bmv4vYw04wPGq31HY9TbZSfO3cu69atY8+ePfzlX/4lpVKJV199le3bt9PS0sJP/uRP3vO5fPGLX+QjH/nImPf98i//Mj/wAz/Ali1bprTvODK7T4xX5FH9Qly5coUzZ868IZZUw4tMxksrjrftVI4JYE2I6vlDgnI/fuUyxltJzuuCyhmstwhhS1gUhB0g67CJleTKryF8gUnvQpb2Y8MiOvMEqnwEE5YIkjtxKkcxpkSYfAJVORj9ndqJKu7FuLMx3jJU5URUWWglgU5iRQZVPk2YWIvyzyLLZzGJJYiwB+PMxhmK7oS+hahcxbqtIJKEyU04g98hzDwR2Vilvxdn8NuE2aeQtkCnv5GWwgF0aj0yuIFO7UBWTmGdGaT9E+jMGpK2hAmSZIJOtOmlP9+Cog+h1tE48AKhtxKpAhLtv4jf9AF0/f8z6dd8KjwOYjaa4b1X169fZ+PGjbVqyeEVfNW05L0YJr+Z0ox3E7PReJ7H5s2b6e7u5m//9m+pr69n7969XLp06Z7PZcGCBWPe/sILL/Cd73yHvXv38rGPfWxK+47F7D4w3JJqdJFHVRAuXLgwZUuqe4nMtNbs2bOHMAzvGo0NZ6rVjNVtnb4/pTx4hXwpTWNW4JoTaLUJKQYQYRdIF2EE1p2PKJ+EcIC+YDnNTjuifBqT2oSonEeWzmOS6xD+FWTlImFiNSq4hqicRXsbkP55RPk0YWorTvkYVufR3hpk5QRS1GOtC0JiVBtO+QQ6uQLp30AVD6NT6xG6H+MuQpUOEqbWIUkggltY1YAQGcLUTpz864TpTdEomdz34Qy+TCWxjqS4RZB5Aqd8BOPOQw3tXwS3MO5sVGEvJrkK4TQipIsUlhkcp5LcgQ4G6As24pSu4okCFTEXr/SfEAOHMTM/XnsdHwSPappxMvuHqIKvoaFhRAVfNVVWLXKY6GTo0bzRI2YmRzcw/nVlKqJZKBQAarMUd+3axa5du+7lJMelXC7z0Y9+lC984Qu3jZSaDLGY3QOTsaTavHnzlCqD7kXMBgYGKJVKNDc3s2LFikn9OruX8TGeHCTo+EsQDtMz1zGJdRhTjyodxSSXIaTFijQi7EAEndjEKoR/kTp1Fl9tICl6EMUT2ORShO5HVC5inJlAHlm5hnFaESKPrJyPKgVNF07xMGFyDSq4giodRCc3IMpnSYoylmUIm8e481GlE4SJZUiRQBVeR6e3InQe7a3ALewjTK3HOjORwS2QAYgMYXo7qngEk1yMrHQQZp/EKRxE22mo8jl0Yi3Cv4pRLajCHnRqI9gyxluErJzHyizGnRW5i6R3kci/gM7sIKnyGLWMMKyQrpwg78/D6/xL8h378fT76O6eRTKZvKPh7FR4XNKM4zFWQ/PwCr5Zs2aNa5g8vA3gTobJj0OaUcrdeM4f4Yf/HmPGFrNqSnayxykWiziOc0cn//vFf/yP/5GNGzfy9re//Z72E4vZFLmbJdWFCxe4cOECixcv5vTp01O29FFKTVrMqmnFy5cv4zgOq1evnvRxp5pm7OjoYGn2L3Edn1R6NpYGVOE1THozJrEYoQcBF6GvYbwFyLADmX8NndlGpQDZ8jFsdg2IDKJyA+tOA+VFERQeQjUidD/I1FBJfjvGmY5wUzjl45HzhkjhFF6hnNiKNudRlVNobznCFDHefJzyaXRiMTqxEif/KjqzHWErhMkNOIX9hMl1GKcNobsRpg9MBZ1ejyyfBWcasnwBP7EGp3IWK1tRxYPo1DqEHsB4i3EKe9DJlViRxrhzwZaj/WY2I3SJIPMMTukIVuUQJsRVWUx2B3X+RayYywz/FBk+y+XOK7x8cXvNk6+pqem+2UM9zuNZqj+y7iQ2YxkmV9sAbt26xblz53Bdd0QbQHUCd/U5PKppRimO4qovIuR1LK0Ys2bcx07GZWQ4+Xx+0qN/psr//J//k66uLmbOjFpwisUi/+t//S/279/P5z//+QnvJxazKVB18pioJdXZs2fvyb1+MqJSKpU4fPgwYRiydu1ajh8/PuXjTiYyqwpo341vszp3ETfRhiwfwSRXYNJbkeVzmMQCMCFW1YFsQuV3R5FRMo3K7yU08wkT9XhBO1ZNA1UHJkBYTXQqDpgiCLBWImxlKMLLg0xivAWoynm0Nx+dXEOi8Ar9ZjlZ5UTl9qn1CFNGu3NR5fNobx5hejPO4KuE2e0I6xOmtuAU9xImV2DVDKwZROp+RKUSrbMFHQiRwS2fYMDMIoPFuHNR+dcx6Y1ASOgtR1UuY2Ua47YihEuY2owz8BJhbhcq6Iyaq3XfUPl/AlU+h0kujoTaa8P4BVZ7X2TJwg7aE/+K7n7NmTNnKJfL1NXV1fwRp7Iu9LinGadiNTV6eOZY88WSyWStBSAIgkeumlFwFk99ASlOYEUTWI9Q33mNtXrdmaqYPQy+8Y1v1MZfAfzKr/wKW7Zs4cd+7McmtZ9YzCbB6Lljj5IlFcCtW7c4evQoLS0trFixgmKxOOUL12SO+91y/wpPzvzfFAYtQgeY1EZkYR8msRTjLUCEJayqR5aOY5KrMKm1qMFXMZnNmPQakv4FLLOwIgvGgAVh+rDuTND9yOAaxlsYiUB4A+POQ+gBsEWsSCCswTityOAmVk0nSG6iWe/Dim1obznO4OuEmW0IW4nWtCpXMO5MwsxOnMHd6MxmBCXC9DZUYR8msQCrGjBOAul3RoKcXAw6j5HTaZCnsXILwvqYxDJk4UAkSKQw7nwwBZziUXRqLYIKQd0/wSnuw3jzkJXLWG8mOrkKWbmAdWZGr0VqLVY1YW2FSnIzyZ7/ybzEy7TM+V3M8qdr60I9PT21daHh0cVEfk0/7mnGiURmd2Os+WLDDZMLhQKO43D27Nm7utRPlYkWZggu4Ik/QMoDWGZgbQNQARJo88/ueozhdlUT5UH0mI3H6IK0TCZDc3NzbYLARInFbIIM7x2DkX5mxhjOnDnD1atXWblyJTNnzhzpSziFVGGViYjK8OOvWrWqFq7fj0rIu9Hd3c3hw4eZNm0a2xaewukL0DaNDC+DaMGktyH8S2AdMHkQCUxyJTK/G5PegMlsjxqk3TmENocyIdgkIryJ9SJ3AFk4gk6txSqBKh5AJzeCclDFQ4SpDUijUJUraG/xULSWAD2IIEVPsJzpxSPoxArCzGacwVcIszsQCMzQ2piR9YTZnaj8Xkx6DcL0o9NbUaXDGFeDasC40WNV8UQkzlJS1K00FA5iksuwJNCJqLhECIF2ZiFkXZS6HHyNMLcd5Xegk5sRwY1IqP0bCJEYqqzsxiRWIkunQCbwdQsZXSHMbEWYAdJnf4hg2k/A7E+SmjmzZg9VXRfq7u4e4aBRjTCGp85Gv78PikcxMrsbo0ewnD17lsHBQbTWnD17thYRV3801NXV3XNZ/d0iM8FlXP4QJXZjacXaZsBHyDyWJrTdwd0u4WMVpU2EYrE4YWuxqVAtMBmLP/mTP5nSPmMxuwvDJ7hWv6RTsaR6UGnGUqnEoUOHxjx+ddupXFzuVs04fF1wxYoVzJqRxD33w1hvHpIBAmclCX0aTBnrtCFMBeu0IYsHMe4iTPaJKEJz52C9OQhdweCidBe487HuzCiqS23EJJejBl8mSG9FJ1fjDL5EmN2OSa7Czb9MmNmO9uYNrV2tRwiJCDtBuCh8THIdqnIq8m/MPoEz+DI6uxkrEminBRl2IypldGYbqngYk1iEDDrQqXXIyhkwAaj6aB0tVMjyKYSahbYptLcEVb6MdRqwqhHjzkXYAk7pKDo15NNY93QU6SWXokpnMMlFGHxkpR3rJFH5vejMZjBFjLcQhGCG3IPPDoQugMwQ1D2D6nuO9MC3qcz9T+j6t425LjQ6dZZKpWri1tDQgOu6j32a8WH4JlYncC9btgxgTMPk4W0Ao+2gJsJ4hRnCXMTlj1DswYgZUUqREEEX1rZijYMQRUJ9d7unyZblV8nn8w8tMrtfxGJ2B6pFHseOHaOlpaU2GbbKRC2pHlRkVk0rtra2snz58tuOX/1yTeXicqc1M9/3OXLkCMVikW3btkW/Uq99HOvMRIQFFGUc/xw2vQYRtoMejEyCTYBJb0EWD2BNCyaxAhH2YBmK2vAI5Szc4iFMajUmvRk58Aoms4EgvQOn8Bq+txayT0QeiKm1UYpw4GXCzGZ0aj3O4G7C7GZw25DlC1ibBRtgEsuRlUtYUyHIfQ9u/jV0amUUKarpyLAPWT4TFXqUzmC9VmT5IiaxFFm5grD9CFHAONMxIoH0O0ggQcyLUqimB1m+gEnMB5GN1sgKr6PTG5B+Ozq9BVG5jJX1yOIJjDcL481Hhp2RQPd+G51di5VpBIZbeiPTy6cRMoFJzEHpW5jUSrBlEpf+Nbr+GSqzPwlOw4j3rBo5LFy4kDAMaxfg8+fPUyqVyOVyeJ6H1vqBFTk8DKuphz38c7RhcrFYrL22V65cwVo76XSvMWZE6lKYs3j2z5AcxIp6LBmE1QjTgxWtWKYRpRfLaLsFy/S7Po+pVkwWCoXHymQYYjEbl+G9Y4ODgzQ2Nj4yllTD04qrV6+mra1tzG2Hp0Ene3EZL83Y19fHoUOHqK+vZ8eOHbiuixh8GdX9l5j0eiDEN82kRBFZ2I9JrQFKUd9W+SyE/UM9ZFcg6MFKN3IBcWaSsfsx4XxMZity8DVMchkm9z2Q30eh0kgoVpMNzjJomxHuOnLFc1hvDmHubajCHoy3iDD3FM7gi+j0GrS7kLQ8ArYJbIB25yLDTlTpEkF2F05+P9abjVU5jNOIDF1U/hBhZgPSv4Z1pqOKx9Cp1YjgFhiNKl9Ee/MwSmC5VSskQU7HJppQhSPo9GoEAWH2KVTxACaxGFU8jk6tiETbNiKCXqR/jTC9FqkHCXM7kP5lVNhHmNmIRzd+YjWuCCLxS61EFk9j3dbo78IxUqffQ9D6c4TN7x7zPXQc57ZZYz09Pdy4cYNisciLL744olR9Mn1Yd+LNEJmNFprhVKO2TCZT8zrM5/P09PTU0r1KqZqwVdsARlOdMyb0EVzzF0iOg8gCFjAgSlhSQCNRZNY7JGgegfmhCT2PqUZmsZi9CRird0wpVUsTDg4OcujQITzPY+fOneO6eg/nfqYZh6c1d+7ceccP3PDIbCrHHb6dtZbLly9z9uxZlixZwrx586ILlimjOr6ASa0bKqWfTkacQstVOF595Muo6hG6HZtchahcGOohW4ww5citvnIVqxrJs4x6fQZRrqBzu5CF41RKA/SX59GY7EU5PtZdT7Z8DT/opdfMI1G5CbIf464m61+MSt+z34OT34t12xgI5tFSOotJLojWydQ0JIM4hROEmU2o4gmEqYDThFH1COHi9r9KmNuJ0LeiCsn8XsLMJqQexIgEqnQc7S4m0HUYL41TPE6YWhFVLWa3ofL7IsGpXEOnNiL8KxinFZXfj0mtwDhRJGhUC27ft9C5J4b8JOdi3fk4A7sxZgHKvwXJJnR2O8K/AiINYR5VuYRJrcJicG/+Z1Tfc/izPo5N3nmsTCKRGPHDZ/ny5fT09NDb28ulS5dGRHbjXYAnwsNYM3uUGpqHp3urhskDAwP09vZy8+ZNzpw5UzNMrv5LJBJkvP3MrH+eRNgFwkNQwJIGoQCJsAmssAg7gGU6liYQRaydjmXthM5tquX/D7MA5H4Ri9kwxusdq4rZlStXOH369KQtqe5XmrGjo4OjR4/S1tY2ZlpxrG2BKR17+HHDMOTo0aP09/ezefPmmhEsgOz4g6iYI7EU3GmApGxbqS/vx+a2IJQAEkAZObgXndmElH0I/xZWpsAGkbAVT5DUlnJyHWl7FVE4R18wCxV20pSuIJPzQeej6kVvBkk3IGkNRixA+wPo4BbdYQtJunFKJygnVpMKzpERhjC9Hqd0AuNMQ6gsRmYQbgJncD9hdiOqcgn8m+DMAJFGp1fi9D9PWPcUwgyik2txB14eKhzx0cnlePkDWOYDCcL0Jpz8XnRqVVT6n92BKh7FePOiSC2zBhH2R1WMpXNYmUInFyJNkTD3PZF4JWaB2whIgrq3keg5jDQKdALp38IkFmJNCRF2o5PLcAb2YJ06dHoVsnyF5IWPEtZ/L0Hrz4BK3/G9rUY21ehizpw5tT6snp4eOjo6ahfgaiHJcMf6u/Fmicym+hyqzdkNDQ0sWLAArXWtUvLa1Uv03PgvzJ2xh5ZMP9I6CFPAyllYstEkchtgsQihARHdbgOgiCBHyLsnfC5xZPYWxBiD7/vjTpi9du0aQRC8YZZUJ0+e5Pr166xatWrctOJohqcZJ0u1AGRwcJCDBw+SSqXYuXPnyPHrxSOo/n/EZLYgymexziyEfxlsPb67lkTpMjYxO4q8EguxiQRqcD8mswYhJYgEIrwFficmvRrKp0hUjhFk11Hqv4pHO4m6eSg0VpewxoDwAAHGB5lGYpBuAtfNkjRlQuagKwM45bN0hW2kxS1s3z4KyTWkwqugywh3erSLxFKcwT3o7GaEfwtRuY71WkAkCLNbcPq+RVj/NMKWCDO7cAZeIMztQhiNn9pM48Bu0HUIERDkduLkD2BSS5ClC+jUGqR/HZOYh9P/KmF2EwIP484GNG7/ywR1TyDDAmF2KyLsQuWPo7PrUf41iqYV103j+tew7mzUwB5Mch7WnRUJbHo1IHD6nsekFmPdaTi9X0cNvk4w7YfRze+CO1yMR3++h/dhDb8A9/T01Bzrs9lsTdwaGhrGvUi+WSKz+2UCrJSiudGhJfsizqxvYEwFHRbxKz2UK9PwKxKh+kmn+kBKPC8BQmCtQGCBCogkkAMqhDw74WPfi5hV09OPC295MaumFavVimNZUnV3d5NIJNi1a9eUrIXuJc1YqVQwxtDb28uOHTsm9WupWnk51cgsDEN2797NggULWLRo0cgLiNWoa78G/k2E6IsmJ4cFbGIJ2dJrhHoZNjkLrMZ6bcj86+j0Rkx6JSLoAplFBDcwifnIoAPVv5syyzBkEb3HkIl5pFIOWB9sCEJiZd2QzVQCq5ojB3yRinrXwh6sTOIQopI5BDmmV9rpKk5DOj7Jwl469TIyqhdPnccm5uEog06twunfTZDbEvkyVjqw7jSE8AjrnsLp/Q5hw5MIUyLMPY0z8AI6tw2hi3TatbQUT2FSy1FhOzq7OSoecVpRg/sIs5uQegCdWoXKH8R6szDuNIQNCHO7cPteQOc2I8M+rGokzLWgCkcwiflkuIgwc9GpFcigC5NciDB51MCrUYGLCBDWEta/DeG3owb2RxFg5RqJ659D936doOWDmLrbx95PJO2slKK5ubn2w833/Vp/2+nTp6lUKuOa+r7VI7PhCH0G1/8bVPg6Fhch+lAESLeVUjkgm86Q8PKUA5cgzFHxSzhOL4YmkgmNdENcNxENlbWWQDzLZC7b91IAMp4p8KPKW1rMjDGEYXhXS6pcLkdDQ8OUPfKmmmasphUBtmzZguu6k97HVDwWtdacO3cOrTWbN28es3lRtv8+6Ei8ROUCotKOlR4EmgG7mjpzE6FToDuwTismswlVOI5JLYv6wEQCVCNqcA86swmRSpMZOEm/nkNddi5px0RCaCoYpxnhdyB0LzqxAOVfQwQXMMklSP8aIhyIRNG/GUUjTuNQS0ALKa6RSC9C0EDr4AEKqS0ElS6cwkl6zWxcJXDcFWT6oypI4c1CVm5gnQaE0YQNb8Ppf42wbhMi7CeofwZ34FXCxEpSthOd3RY9r+TcKLLKrEIEHZjUctzeF9D1O4AQk1qBCHtR+cPozHqELhLUP41TOBEJtWuQwonSsP4NtE2QCPOo4Bo6vXZofVEQZrZGKUaVRGfWIoNerGoiqJuDqlyKJgEkl+L0v4waPISufwK/9UPYzMraezcVsfE8j5aWFlpaWkaY+vb09HD16tVaNV9TUxO+709q35PlUVszuw2rUf43cIKvIc35aB2MHiCDlY1A9APNlV1RwYdoI5nwEORJZ5qwNokfSLTuoVAaRMoijkqjvCxF83Yy2Ym/f1NdMysWi3Ga8XHgbr1j5XKZI0eOUC6X2bp1K+3t7VNOE8Lk04zGGE6fPs3169dZvnw5x44du6f8/WSOXSgUOHToEBBFdmN24RdPoDr+CJuYjyhfwCYWIXQfiCSifJ6kFfhyLkpo8OYhB/djkksw6dUIvxvr1CNKZ7Gp6DbZt5teuwSjZ5Nzy3huPegBrJqGIEQUT0dl6eYmTv4AYWZjFM0N7CXMbYn+LhxGp9cjwk5E6TImuQjsAKFNIoNurNtEmNtCZnAfQW470tTTXDhNyV1K6Jfp1Eto6n+dglqG67TgBV1IlUZon7B+F2rwACa9HFW+TpDbhTN4iNA2o4pnhiKiKxhvHk7/K4S5HQiTJ8xtxOnfi0ktxKosVk3DpGfg9L1M2LAL5d9Cp1eALg7ZWS1CFY6hU8soW0uKEJ1cjtP7Aia1AJOYHaU8sxvBhDj9ezCpeWAFSvdjvZkYby4yvBmVdqtG3I6v4HR/nbD5Wfy2n8aml9be26kynqlvT08PnZ2d9PX11T53VYG7n4a1Dysym3QFcHgdx//fqODbUW+icMD2Rz/y5HQQGkyItB0YNYdK0EzaU1HpvWzEikYELlL0kUg0IWggk00S6jRhWKY/38ahU5cQ4vKIYpI7NTe/lfrM3nLDOauWVL7vjylknZ2dvPrqqySTSXbu3El9ff2IasapMJk0Y7FYZPfu3bW0YmtrKzC1da/qsSe67c2bN3nttddobm5m3bp1Yz/IBKhrv4lNLERYDaoOObgv8kjUBWxqNQKBE95C6BIEA5jctihq8geHSvEtNrkU2b+XwPfpCheTphNXOSBcQILMIIsnsKoB681C9b2CcZowyUW4fS9gVBMmtRS39zsYNQ3jLcDpewkrm7HuDFT+EFbVYa0zNOG5gDCGMLsNd2AvFgebXU06OEU2V09zXZogs4WcPodfHqCnmCWfz1Mp5zEDlwgyGxHl61iVw8mfJEiuwbMDGHcmauB1rDenZkjs9D4fpZQQ6Ow6CPNR4YcFYTVBwz9B5U+AFcjS5cgxJL0OEfRENluD+0na/sjX0fiEuc1YoXB6vwNWIXQBISCsfwKLgyxdwpJFFs8jK5cxTivGawNCwvRqdHIJ7s2/InPoaRJnfg63cnpKn6XxqFbzzZs3jw0bNjBz5syagF2/fp1XXnmF119/nTNnztDV1TXCh28qPFKRmQ1Q5edI9P88yf4fR1W+BaaCYDD6LMvG6CJrQ0TYDbgYOR0suGoAKXysmAYkEKZ/qNCjHoGMUouAoxTJRJrGGf+WJ598knXr1pHL5ejs7GTv3r288sorHD9+nPb2dsrl8ojTu5c1s6lM+XgjeUtFZsN7x4YPzqzeN9ySarhf2L1UI1a3n4iY3bx5k2PHjjFz5kyWL18+QogetB1WNRKs9s2Vy2WstbelpGT7F1ADr2JSK6I0o5qGTS1D+LdAphD5I5SZQ0r4WFmPKJ2DcGAozdaDlVlk8TTGnUPe3YAzeJxMYh5eaj7B4ABGZBDF89jUEmxqCbLvFXRuGya3cahkfis6tw13YA9hdiO6bvvQ7ZvRuS04fS8Q1O/Eplfg9r2KtksxKovyO7DedISx6OxmVOEwJrUUndmIGjiIzq7BEwGmbif1+f3o1Bx8MQtd6SH0i8juQww4i8iEPUh3Bl5+P312IWldwaRW4PQ8P7S2ViSs24bTfwCdWggqhU3MwlqNM7APXbcFGdyK1tMq7Qgbgt+LtLfQycVI3YtJzMdWevAGXkM37Ih+FKgGgsancQYOgQCdXo4sX8W409C5tshNBA+rmnH6X8O6TejUMoQtgtVDgujg9HyTBcHf0qg2oPp+Gd3w5JQ+V3cjlUqxaNEiAIIgqBWTnDt3rta8XS0mqa+vn1QU9ChEZrJyGFX+Gk7wItgQq+qJJpxHY4OwkUmAFQbIY2UTQtaBtQgzgFUKP8jhpRII04uVOaxoBBywHcCMqMfMBCBdLDmMWIYU3GaYXG0DGG6YXI3agiAY19LsTlTtrB4n3hJidre5Y3fr3bqXAo7q9kEQjHu/MYZTp05x48YNVq9eXYvGqttOtYgD7u6xWLXDstayc+fO2gd4+Nph9W8xsBvZ+4+YzKbIzcJtHfJNXIVQOaxIIbxWspUzBCwG3Y/NrEaULyJKl6LCirBCmFqN7d2DNg24detI2T6slTi2H20S2OxSZN/rmOx6TN1O1MBeTHolYd0uVP4oOrWYMLcVVTiNTs0jrNuOyh/HpBYS1j+FO/g6YXotQW470/peQJsdGG82qnwek5w/FEGtQxVPYtxWdN0W1MBBTGY5IuxDZzeh8sdIugEm0xpdmPwBEpVzDNrF2Hwf1rYwjSOU9DY8G2BzW3B6XkDXb0NYjc5tQJSvIfxb6OScqAet/qmo1yy9HKdwGpNahKEJWb6GdWfg9r9MmNsE0kNToJLZSrLnFUxyJjY5CxkMRpGe8VHF05FfpN8O1qKT8xGuQYT9Uc8bAqf3O1i3Iaoe1QMIqdDplRTKIQn/BsnTP4tJzCFo/THCGe8BOfmL3liM/gHkuu6I5u1yuVxbb6taQw1Pm92tefuNisxEcBGn9BxO5VuI4DrGmQEyBbaAtQohUgg9gHU8QA0VLkUuHpFxdgkrkyAbwLooURryEo1ETJhbUWZBNAEa8IFUNDFd/fiY5zm8Obvq+lJtA7h8+TL5fJ7+/n6CIJiwYbK1No7MHkWq+XxrLa7r3iZkN27c4MSJE8yaNYtly5aN+WvsQaYZi8VibY1quJiM3v5eIrPxCkA6Ozs5cuRIzWV/eDpieI+alBL0IM7FXwRbgKAP67WB9jGZ9dGFNbEQMeQqXxZzccMiQrmIgYPo7NqhOWZgKp2US9epyOU0pnujX6UqBcbgi1YywWnwl2IankD274l8DHPbEKWzCDU96qvyb2KdBnRqEdLvwTo2ilQqN0A1Rqa++aNobxa3zAZaB/cT5tahU0tRhROY1GKEqaBTK1ClC1hTRuc2oQaPYFILkH4nOrMGWTqHLF2JIiuvCSFdGkqn0I0bCcqD9BYW0ZzfTRfLUcLiOGvIDhyH5Exw0tjkHIyp4AweR2dXIXQXOrcNWboQVWAWTmG9GVFDd9hLmFmP07cfk2giMA1IWyas34kIe1C9e9H1W4b8HOtq7QSEIdabidO/B5wGdGY56AIQEtbvABNEBSM46NwapH8LT2sqoh6dXoowg3g3/hT3xp+hG58hbHkfZmhdbarcrcAkmUzS1tZWmxBdKBRq4lYdojncLHl08/bDjMxEcBmn9A+o0vPI4CxGTcPKLNZpAGSUTraVqJpW1SNEIhpPJJJR/xgeoMEKIIWwgqjUXhOGqaHHDWBlZmisi0TYbqycAaQR5DFiDka8bULnPdow+cCBA6TT6dqIpnK5TC6XqwlgdRllNA+qabq7u5snn3yS5557jnnzIiPxr371q3z84x/n6tWrbNiwgT/+4z9m+fLlk973m1rMqr1j1bEs8+fPr90XhiEnT57k1q1brF27lhkzZoy7n/uRZhxr+2pa8U5CCvffDstay7lz57h06dJtKdUqwyMzAHXl01iZwMpGZOkCwu8BU8HqDCa1DBHmsYmFqMGDWLsAsBinGSkc1MBhTGYlQbmHvkIdDV43GXUNm1yJ1XnAQfjXcbRH0V1DXfk0Niyg67YhixewxmCT86HSj6CMUXUIYxHSYFViaFRMiHGbETpABP3o9Epk+SpJG+LXP4U7uBeTmINOr0blj2FSCxG2jE4tRJbbkYXT6Oy6yDIq0RKl8JKLkZWriPJl8Noi26vU4qioI70agcLUb2P64BH8xAL8IKTPzMMd7MSTHWhnBipZh63bipM/jEkvQ+VPDolIPkpDheVoMnbdRoQuoLOrwVaYYQ8SsAsRDIBTR9D0NlTxNMIYrExHopych3GaEGEvJrkIKz2cnm9jvRZ0Znm0rXIIctsQNkSWLiHCIlrOIWE6UYVbWHcaxmuJ1kL7X0P1vYxNzCJo/Cfoae8YauSeHJOplhRCkM1myWaztebtatqsvb2d06dP19JmVXF70JGZLB9lXvpvmDb4WbyBy1FxhtMUGU1jsUIhrECENzBuW5RCxMcKJ/r82f5o8CoKrBoSMo2VAAGQinrIhA+2jJV1YB2EvYmVLRjRHKWHhYu1abT83jv2DN4Jay0NDQ21bE81Ku7t7eXkyZMEQVBrsahGxVLKB1LN2NXVxXvf+14uX75cu+3ChQv87M/+LF/4whd44okn+NjHPsZHPvIRvvWtb016/29KMRvdO+Y4zogL+nBLql27dt01p3w/0ozDj6+15vTp02OmFSey/b0cuzo8tFwus3379nFTCSMis1v/A9X119EFPOjCpJYiw16sMx1RPIm11ddGorMb8frOomVLFB2lVyLSSygP3qQSaJq9PKJuLQRdiMJFbGI6wpaxqcW45UM4fh7TuBlRvIgsDjVd6wI2rBBN5ZQIlUSUoynUVtYhK9exzgyETIItgsgidAnjtULhBqpweaiE/hhWl9DZdajBo5hkVB1ovFZk2IsaOEBYtxFZvhJFTsWzURQX3EKU28FtwKocYWY1Tv4MyjYirMbk1uOWL+G6CdKJLFotIvQLeKVzFIIQbBehu4Rc8QbCnYHbvw+TXYnxZiCHhNfp+ia6flt00RIpOuwGZgweR7hZjGhFhYOY5FIwZWT5OsZrQxbOAIIwuwphKtFw0bqdoIs4va9inUZMZgmqfBPrpDGppYBB5a+DBePNhXAQp/clrEpj0kuj6KJyA6/jL+DW/8Ckl6LrnyBsegac+gl95u6lz2y0e8boOWPHjh0jkUiglKKnp2fcyGJS6AFU8RVU6RVU+TWE7mSGmwA7C+vMjdbEkEgrEfoaiHqs0wyOBKJji7AboSRWNoDwAQd0CWQ6akMRFmFdLBYIEdZgjYckiTCDQ2tm0wCDsIMg6ojq80qE8s4DOO/41EYVgIyOikulUs3S7OrVq3z0ox+tmapX6wfuVxT8gQ98gPe85z3s2bOndtvp06f51Kc+xQ/+4A8C8KEPfYh3v/vdU9r/m07MxrKkqqYJrbVcvXp10pZU9xqZDRfDQqHA4cOHEUKMm1Yca/v7sWbW09PD4cOHaWxsHDE8dLztACieRnb8BSa5DFG6inWbUYOHMOlViLAPk1kbpf1UA7JwHOPOJJDTUNZgMiuQAwfp0/ORaDK51midoPc1TP1m8BLRr9ZgEFHuoqiWkDQ3EQNHsZnlCJ2HYBAEIFQkMJUrWN2ISc6LohOnBZOYjyqcxHgtWHdGJEZOMwLQ1sO49ajyJXRmJbJ0GTV4jDC7FlU8A04OJBinESE83J5XCBp2Iv1bWK8VNXgMnV0RuZX4vdGAUW8aYWopbv8FhC+xTl3U1Bz2Isvt4Glkog5SW6gfPE7gzUaULzNg5iEGexBiGpm+EwgnQ5hZjLJlwoa3oQrHovWvzHI8WyDIbsChiCycHYrqTmASrZjMEkTQF6W8vAbcrhewiWno7EpEOADCJax/AqEHkfkTkW2Y04AqnMKqLKFoJJSNeFiQLmF2A0gXVTyLCHojYcsswwKq7zXkwAHc63+CSS9B5zah63dhM4vH/ezczzTg6LRZpVLhzJkz5PP52yKLavP2XYXUFJHFfajyXlRpH9I/DdZEUZZqApnB2C6EUNFzCa+jQoXxZoMzb8huSiJMBWk6ozFGqgVkJBoy6ME4HlbWDa2l+WD8qESfAPAwNkQQggijYbQohOnEyhlYUY+0PViaMOqJIfePqXGnpunhLRZVw+QvfelLPPfccxw/fpz3vve9pNNpnn76ad75zndOevLzaL74xS+yYMECfvEXf7F22zve8Y4Rjzl79mytcGiyvKnErBqNjS7yUErh+z6HDh2ir6+PTZs21SbMToR7XTOrimF1ZMzd0oqjuR+R2cWLFzl37hxLly5l7ty5d/3CCyFwRIXkpX+PYAArG7BeK1gZrfGUr4GTQQ4ew6aXg86jsxuRxbMIncYVvYRlQX+wgIzsI5GbjSqdQWdWILJrEYUL2OTsqBw9MRPp3yI7eJSCt4pE0kZl8G4TQoBVKUT5BtI66MQinMIprO4nTK/GKZzAhoOEmVVDfxeida/C2WhdzSaidJ7bHKUOE7ORQQ9O3+vohq2I0lXQPkIZUBl0djVu9/OEzW9DBP2Y1CJU/0F03Tqs5yLCQWTpKtppoSRaSAmQ5XaM2wxuEzpTj8qfxggQ5Alz63BKF7GZhTQPHCJo3ELolwgCjzD0yfW8SI9aT9IpoLzFuA44fXsxdiGqfA2bnIGu24wsR4bNhGVUcR86uwq8VOQFWb8VrI/T/RIm2YpJzUf6HViVIcxtQuh8JM4ijVWNpArHsEKBXoR1p0d+l8bHJOdj06sQtoIoX0WaAggHm5wX9bV1fwOn51tYmcQmZ6OzazDZDei6TdjU/Npn50E6gCQSCTKZDK7rsmzZshGRxZUrVwBuM0uWwWVk6QiqdBRZOYqsnImmjTvTsE4zxl2IsKUhC7foX0L24viVaN3TXYAwBbASawOkvoFQzVjZBCpJ9GvIR+p+jDMzEkThIMwg6BCrMkBYfXFAWKzV0doaCbB9IBqwshlsKRJR0QhCE7gfvKfXazKl+UIIduzYwbx58/j85z/P4OAghw8f5tvf/janTp26p/MA7uoo4vs+X/jCF/i5n/u5Ke3/TSFm1d6xav/K6CKPIAjo6OigqalpSpZU95pmhCgiO378+IRGxox1/HuJDC9fvkwYhmzZsoWGhoYJb7fM/Uq0sJ1oQxZPRkUeQQcmMQe86SBchCcQpYugcohKNza9GOHfJG/ayORPkfXmksjMjNJa6eWo/v2Y7FpsYhZYg1U51MABdG4DFQdS/tloDpojoqgtLCOCPmxiPpQuRpFSbg2yfAln4DC6bh2ydAln4BC6bgOyeB7VfwxdtwZZvEjK5rFqKYT9Q5FdB8abjkgncLpeJGx6AuF3IvxerGtBpggbtuF0foOw+RmELqEza3B69xHWr4sEUqZwChdQpgGc2WinDlU4F63lODl0bi2ycAbrzcAZOEqYW4sMutB1a3F796AyCzHpJpI2IBSzae59maJcSCXfScG6WHcDKX0eG6aRfh/C3ozW+EwZEfSiM6tQ/YdASHT9JkRYAOkQND41lC49gvVmgEiiCmeidGNyIZgSQufx1Ux8kaPO70QNHh0qKFkB1iCDLqxwIx9IFYml0P0IU8HIeqzXHF2oy514A18G/hsWERWyZFdhsitprGRwg/VgZ0XGufeZ6prZbZFF0Eu55wjlvhcwnWcIblwg6dzAcUooYbBeC9aNxAsqQ0a+FoiKpGRwHSFcjDuTQtBGMpeICjasBd2HDDsx7lyMMy9qgBZRehGbilpUrEsUYQ1grcGquqjHER21sYgGqq290ZqZxWIQIh0dw+RBZofW2XoxzpNYcW/+iFNxACkWi3ieRzqdZteuXezateuezmGi/Pqv/zqZTIYPfnBqAv7Yi1m1d6x6sR/+xlUtqdrb28nlcmzcuHFKvxjvJTIrFAqcOXMGrTVPPPHElHo3pipm/f399PX11RrAJyPi8sYfM00eIXSW4JoCOrseWb6BTcyPCijSyxHlK5jkfKRIRqNcrI/InyIIsgiTx9ZvJalvYLVFVK5gE62Yuq2I0kVsYmbkg5iYjUmvQPXsRrsrMM483KAPZDJan0vOQfqdyP59UZQhbuL0vErQsB0pulE9r6EbtiFEBqf7FYKGHUjRgdPzKmHDDkz+DE7+JCa3FhF2Y/GQfi/GrUfXb8LpfoGw8cloBEflFtZtRqgkYePbcDq/Sdj8dOSlWL8Fp3c3un4dViQI0svI9B4FP41w6tCZlajiGSwCEQxgMssQ5RuY5ALc7hcIG3dFPWi5tcigE1W6iq7bgDJFdNP3kCpdJG16CVILMX4PfXY25UqFVLmL0G0lV3wVk5qPTc1C6EFMZvlQwcfLUU9ZdhnS7wKZRtdvRwTdiHIH1m0AHaL6dmO96ZjkfEIpUdbHui2EqUXRGJ/CGUQ4iPHasIk2RKUTaUsgUxi3MRJHqxGmGPllOnWE7mqQGawgEr3SWZzCEeaXi6gyOLc8THIWJjEHm2gbciiZHq11us3gRGuQOJnILWMsTBhd5HUeGQ6A7qWuchxl+3BvSGTYEVmdhe0I009Wl8EGmGQTJtNAYOZQ8X10mMdUAlC9OG4GzxN49CLJY1V9ZLnmLUHYYlT0ZA1Cl5DhTbQ7G5zZUSWvEGB9ZHAD487CqFkgguiHQNiBcWZg5DRAIEwAdiASJJUZErYwEj0biXEkliWQHoh6hO3DigasaCRwfnjS3/nRTKVpOp/PT2i46P3kW9/6Fn/2Z3/G888/PyXbPniMxWy4JdVYvWPDLanmzZtHqVSa8psz1TWzalqxubmZ/v7+KTchTlbMhq8NptNpWltbJyVkou8V1LUvoUnglE5Cau5QMcYs0CVMdi3C78Am5kSVirnViMotQqeNQrkdaw0pJyRROY/NLEboIjazFNl/MCpzT8yO1hCSs5F9+zHZNZj6LST7z1JWM8AMVSk6Dai+fVH0IRI43S8QNOyAXBqndw+6YSMmtyZKA+bWoHNrcPr2oOs3onMpnK4XKLGCtNeI2/caYcN2RNCP1XlEmB+Kwnbi9LxE2LAdm5gVCbbXGA3XnPZ9OJ3PEzbvQugKYdMTOD2vo3PLEVbRKxYyo9KBAYRQ6PQKZOki1m1E9R0mrF+HDPoJ67bgdD6PbtiIEA7Wa8F4bTjdL6IbdyLLQ9FuYhZu/iQ6tZj64imchsWEsgW3fItBMweR7yWTP0MhuQbHVXgqIGjYhdB5VN9+rDcT67rI4vmoSjG7EhH2R96VqWWAxul+gYxwKXpLsCqNCPpBOpGtlkxA0I/0b4EpRqKjMsjyzaF10STWqcckZoJKga0gwr5oAgICZAPGbaVQKeJ5KVJJD2yAqLQj/atREET00O9+2Ib+R6ihfwKqwynRYDUwFN3YEGzATD+PtD5OZw7rZLEyHRVQOHXgaIStRKeDxXUUnlsHJBFBJza8RWigkG+mT6dIeGk81+CYEspJImwRGfbgiCRWzcOKuqFTsqD7Ebof47ZhnNmRG4sNELod487GOjMjUTaFSBTVDJAycv/Qg1inGUuC6ogXbPX5p8D6UepX1IEpgzM/yijcA8YYrLVTFrOHxcWLF/ngBz/I5z//eVasWDHl/TyWdlbVIo+qJdVoIevs7OSVV16pRSSZTOaeqxGr4jkRtNYcP36cEydOsGbNGhYsWDClAZnDjz/R8w/DkCNHjnDu3Dk2btxILpeb3LFLl1BXfgebmIWxHtptjS4oViDKNxBBT/SLX9aD0VHEU75FxeQwvXuQbo6kq/DlLHDqEMVo7ArlTnTdZjAVCEuIoBeCMqZ+W1SVFxYInBlIHWKdeuTgCSCJya1Cdb2MFR5hw1acgaOAG6UXCxexVmAyKyOxRaLr1qEGT2HxCBu3Mc2cxMgMYXYdTtd3sCoXTb2u9IMJIu/Fxidx+l6PigCScxGVvui+chfBtO/F6T0YVbP5fYRNO5GFiwjt49k8OrcaEQwiLMjCOXRqIUIHmPSSqDDDqUOYgLBxJ7J4FVm8gjUmsrWa9n3I/GkwAbJ8ExGWCHObkDpPhRzS7yZZOIaXaSNb10y6ro1Kbhvp8hm8wWP09JUo9VylXPIpZ7ZinEzUgC3rEX4vqv9g1AuYmAUysgnT9VsoeCtJ+FdxenZHqWE8pN+FLF9D2BCTnIvJrMLKDMKUQWbQmdXozJqoAKh4FtW/G6d/P7J4CUIfaz3AQQR9pPVlkv65qE+vcg3pd0JQAmOxwosmHcg0Ruai/iqZwZLAomprVtYqsEOPJY0hi5ENGNlIYBoIZTPWqY8Kc7BRMQUCRAIrMqA1wr+BUzqFLJ0CXcG6MyG9Eje9gIa6LE2N9STcBOhBdPE8/b036CskKeoWIjcPHb03fnskNs5MkHUIaxGmhAhvYqSHVa1DIjaI0N0gs1FV4zALqyjlGERCZV2wDlKaSNCq3y/rgIlK8gPnvZO5RIxJ9Xo1WTGrzjJ7GJFZqVTiPe95D+985zt59tlnyefztb7gyfLYRWbDLalGi9h4llT3o4Cjuv+75Z+rRr1Sytok6sHBwfta2j8e+XyegwcP1qZgJ5NJ2tvbJ/7BCAdwTv+rKCXotpGgH8M8BGFUOKH7MTKLLF0E6SEqXVinmUKQplQukMuuIqc7KNhGUv45THY9MixEKUj/OqJyAptdFpXae7ORA4eHUo8bEOUbYBIo0wemHpNdhezZjalbh2naieo/QphajM6uRJYjayqbaI32rzJYb1rtb51agCzfwnpNdItlTMufxGaXEjY+gdP1HcLGXZjkzEgAU7MRQSG6r/t1dN1yTGpeVHDhZFDFa4RNu1D9BzCZxcjiNcK6zcjB42CTyPyFqLqwfB281ihya9yOCPsIG3bgdHwT3bwToSvozBLQJZzeg+jGzchyBzq3HuF3ISu3sCqNkz+OziwnEBYrQGdm4dx6HpNbhE3MJGEq2IYNIATT+w8TyizFMIntO0OBOoS3gJRfwLMakouQfjtq8AQmORuTnhcVsBifsjMPWTcd4fcgi9GEbpNeAFag+g+D8qIqzUQrxnGii7cug1DRoFCViiIpGyDCAUTYhTAhoLFGoUUDwm0cWjOzCOODKSHD/mjtzvrfrVIV8ruRmVSAAulE/VyoyM5JeFjhRNG0EBgh8aQXFW74vQibhyFBM950jGoEZykCjbBlhNVY64NxAIMIO3CFQiZaEWoRmBKuLlIJBWHgkxD95Ps01p1G0m3EkSFSOGD6AY1RDUjhIgxg+0H7kSO+CEEHCHMrml2npg2lZ/uxcjpIFTVTWw+sQ6RmCaJGageIGpWNe+82Y8MruifDw3TM/+Y3v8mpU6c4deoUf/7nf167/cSJE7Wm6ony2IjZ3SypqiXvwG2WVPdLzLTWdyxnv3HjBsePH2fOnDksXbq09iG61wKOiWxfPfa8efNYvHjx5I9tQpzzvxzZ8aSWIIrnKdtG0uWz2MzKyE9xqL/MpJdFhQjJxYS9R/DtNJq8QYSTw7pzoZinotrI9R3AZFdHFYvphchKB6J4BdwchCVM/WZE/iSiZLBuI6JSxJetpAaPYdKLMc1PIvsPYVJzMbk1yFIHxq3HOlmECSPTYtMfRRAiAeEAiBRCyKgcXZdRJiTILscrXcN4Mwibn8bpeomwfgMmvQiVPxNd5P1BwqbtqN4DmNRsTHIOonILVAo1eBpdtzEq6ki04gyewE8vQ5VPYxOzUX0HohSi34upW4dz6xuE055B6CJh89uiIgu3KXreKk3Y/CSqbx8mtxyZP4tJz0c7jUON2nNwul/FMTMw3nyUKRI27UAE3ThdL6KbdiB0IbK8atiG1H3UFa5gcrNI+gPY8CJFPYMBXYdX6cVTCURyPR6DuF0vYVUSoxYjKSEqHSCSmEyU2hFhL0IXoyq/xDSEKaH6Dg5ZLrmY9Hys1wTCIIIeom51NdQ2MT2yahKKQqWHtHJwraFWxScEiDRWRql2O1zIqgkiQVQUYaPIFYJI9MJSlM6zFbABGV0B7SHUdKyTw3qzoshZaLBlEAZpK1g7JJKWaJpCoLFOPdadgU3kEKaANJUhU2hwbB7lJgi8aQz0Q31OUgktlXIRv9RPIKbjeVk8FxRhJGyOxMqoPwzrI3QP1mmL+h6tQegurDMTIxsRVKPTNMaEUerUWJACcKL1QeUSePdWAl9lLA/aifCgHfMLhULt73e+850j/v9eeCzEbKzesclYUt2rmFWPNd4+qpOgOzo6WLdu3W1uIlVBmWrJ8p0EyRjDyZMnuXnz5h2PfTfU+V+F/CGM04IM+jGppTjFKwSJpSSCHqw3Fzl4Cpuei+w/gp9YSGngEsZdTEMqBHcWsv8IJr0IN+ymTBMmtypao5IpVN/+KAKTxcgpwb8J5aPY3GpE0A1Go3QPxiQxTVuRfQewQQGTW4eotBOGUK5YCIq4iTRe0A7JWeC2oPKn0Okl4LUgC2fQ6cUIpy5qrLZe1NicnInw+6OU37S3oXp2YzIL0NnlqMFTmPR8RKUH3bARNXAcqyuY1OzIusttRvUdJKzfgCpfxyTn4PXto5dFZLSPzq7AufUdwmnfg9AFwmlP49z6Nrp5ByIYRA8Juhy8gMkuQlIkbNiOKlwAlUUWzoPKYtILEX4PYW4lTu9V3N7X0U3bI/FSjYTN34saPAwmQNetQpYuR8Uf9esRfjcKi8kspL5wnnpZopJYRMV42FI/pVCDuxpPWRL+ZRxTBG8pVoEaPIlVaazXhEnMwtoQqYuAxGQWR9MHsEi/EzV4MioAsSYq6nCbIrHw+6J0ojDU6RBV8ZDaGxp9kwaViMr8R1Q3mmgtyoYghtaQsFFvPNFaUiR+AoRAYLDCUMr34zoCpVIITJS6k0ksEnAQYT8y7MIKB+vURWtV3hKgPJQeHIjOy4ooUpSVSODc2ZFzvS4B4MgQJ+li1GyEyRKEgiAMCcpd9A824LkujufjOiGuKoDbilWNUaFH2Il1Z2GdaZHImUFQjdHz0N1AlFoVtoIhjbAMPe8U2n3nZC8RY3IvjvmP2ywzeAzETGvNzZs3yeVyeJ43Qgwmakl1P8RsvCKQfD7P4cOHR6QVxzo+TH3q63iCVPV1rPaHjFVgIoS463OXl34H2fV/sckFUZNtcg6yeA5h3ahkPdUI1mLTC8GGlMV0gr4LJJJ1JLmGlfMRlV50/XpkpZNAtZEunQC9OkoNiRQmsxTZdwRTtxzhd0e9UJWbiIFj2OxihC4TuLNxi2cQ+RBTvwlRvIIodVCxSQr5PG4iixfeoFCuZ0DU01g8QpBcgEqtwOvfh8kuR2dXRVFPZjkmOYfM4GGwOcDBqDTSWmTxBrpxG6r/KDYso7OrkPlTUUFK+RY6txpZOI/Mn8dkFkFYwKTm43a9Qti8A+H34GdXMaNn9/+fvT+P1etK03ux31prD988nflwnkSKpCaKkkpDjd25DpIYMZwuB3Gju+MENzYugosbxzCS2DftTmy3g8RJAHcM98XFBRoeroEYvojt2Ia72l3VNUulEkWJEimR4nh45m8e995rrfzx7nNKqioNpFTd1UgtQCB5dL7pnL3Xu97nfQZc+BVUNhRyyMZ/IFv8isCWC1/GdC/jC4sol+RFp4XpvYmrPEIwuIqtnMqjaTK8KhDsfIes+QzYGQk1ktpp4p1vSmdaWBQT5Op5Kfyjd/FBE9IeZrKGKx7Blo6hbR9fWMaFDeLhVQpJG1c9jQ3msNM2qVV03QEcmvJoRKzb+KCAChbQsy1M7zI+KOELB3HRnEBk2QClNAQVbDQPOsIrh7Jj+c9nMm80dXxUZZCmFKMycRhIN+UmQjRxE+E77BFG0NKVqOBHHZ4yKGUEnlRaWjgdSmTP3tyPFKOQuZhto/xIHkuEi5dwwQIuWEIxExjSDYRwoRQ4Kw4bXtAAFx1Cua4gEqYCHrQbALFYUtk+SiegFJFJCeI5tDMUiUmzMdYO6Q+LaCw67FCM+uhwlSCYz4taBx8ugmqAG4Auiq/jbAL4nAVsxbqKGTb4Tz4zOcPD7jd/GoM54ee4mL1fO3b58mUuXLjwgYC/fr/P66+//oksqT5tMfuw59iD9g4fPsypU6c+0lsRHv7i+mmFdGtri8uXL38gLubDXvujZmZ67b9Gt38fVzyFzob4wuE8WLAkBqp2CKkwwVy4xHTcZpyWqNcOEYRlyDqopAd+ih5JQKR2fQbhGZqzLXy8ih68jSufxlXPQDrGq7KwFGsXULqCSkfgU8Kkyyg4SaQ6qO5buOoppsNdJtMJ9UKGDj2+fJZW73WycIGJepLi6HXGow694Ayt3jtk0TKu9oxYRsWH6JujzI+uQ/k4BBV82oGggp6sY2vn0cP30INruOqj6MF1fHEBPb6HKx9HT+5j+m9hK2fwPsHWHiPY+gbZwhdQsx47+hyL6/8Bu/RLKDshW/plgu1vYxtPoWa72PrjqNkmerYrpA9TImtexAxv4KJlTFugRhevoNIuWeMCwfY3ceWjOGK0m5K1Po9Kdgjar2GbF9DjNXwoWjaVdlGzbWx8GDO4hsbiqudwQRFlpxLoWX0MM7lLOPwhJmoRlI8Q9G/jVYgPmwzsHG4yJJxuExqFjs8QxGXMbItg+D3Z9IMarnwMryJU0hV6vg7loGJKuKAEWuY/3qdov4XxM5R3CK2wKN0Z5IebvFApxY+ojR7pxyweKzIPOwY7zuHFDHCgoJSC1/P4aB4fHs/p8gJDCruwh1elvHj5vCDNcGFLujRfQbmeFBpTxfsQ7SdCRDENfLZJoCbga+Q3bq7/2kX5LCchZkRxA+UDiuUSLktJbJFZmpGMe8SmizNLRHGZkDHaOJQpA0Ze18VALIQoU8x/DDWy+H/ywPvDh63/fwrmhJ/TYvbj2rH3F5L3086PHTvGiRMnPha6+yyK2fsZhR8HK/60x+497mE0FO+3pNpzv75z5w7nz59nZWXlY1/7w2BGff/3MGv/tThtJAO8CYRurDw+quPVOkl4nJIaksYnyDpXmKkV5sN1fHAGNbmHKx5GqTHoJdRsHdI+ge0QpQpfPY7KJjLv6l3CVc6gXJrHkjyK6byKqz+O91MI52E6pTp5A1d7AXSXSfsWmQ9pVMqoeBU1uAZpH9u4QNC/QoURdv55qoO3KbkthvHjxON3SMZdevEjNCa3KGWapPkEhdHbuGgOX1hCzTbwQQ09WceVjqFnG5jOq9jG06jJPbypoIe3ZJZGlIuwzwCerPkMweYfkrRewPgB2eIvE2x+g2z+eVTSJ5t/CdN7S+j9k3V8YQkbtjDD67hChBm8I5qw2Y689vAWKLC18yg7JGs+h0p2mMuuYPVL6DyZO53/Amb0LspZfFDDdC/jykex5ZPorIeLV/BhA9O5hPIzbPMCHoVOe/hwjqx4RGj3kzW0nZHEC5TpUXJtfFwjCZeZWUMy6+HHI7TW6PBRwrhMpDL0bEuIFHaWQ3dVvNKodIgZ3gA/yzsKRdl6dNKUqBMjGsQfGeU6cJl0I3sFyjuBGfMCp1SA15FAn2YBpfeKngOfMcs6RDoUpqVP8lmdBq/BzgTS00V80MSbppA1XA+d7uJMBXRJID47ldfVNbzL0NkuLpgT2A+xBUPl3omqIf/2Pv/aBK88e4nSRpcohBEFq/HVFjYrkGQeO2szHBXQWlOIO+hogSisotgBRFag3AQo4aLnQP0ksvOw62EE0/ALmPEzWe/Xjr0/BToIAqy1JEnClStXHtiSaq+z+TQ2O3sFcTgccunSJYIg+FBY8cfXp80k01qTZRnT6ZTXX3+dNE15/vnnP9Hp6cOKmb7/jzG3/28QzaNmbXBTPAuo5Da+eBw1ehfr5ygl95hEB5n176KLJ2nEFm8eR03v4OMVTO91XOUcanJLbKTsgDQsY9KbqOm2bFg2wdUvoKYb+LCF7r2Bq57F1R8XGNNU0P23SINjuNBQab9G2y4TByWqlZaIgYc3sJUz6NFNdOc1ssaTmPE9gu7rZPXzmOkW9elNbOtxwuk68eQWw+A4QXoXdl+lUzhLeXIXk/Tx1UfkvZgKerqBi5dQqkCw823S+Rcx0y0pDIPr2NJRbCnC9K/iSsdQOiCbe5Fw92W8Po7KBmSLX8R0XsNVjqPHG9jaWdR0C5UOUXYN4jls9Sx6dAsfrxDsfAfbEjjRFVeAgGDzD7DzL6HsFB822TZPsNR7Ex82wWtM0sOVTuVGw+u4+CBqdJfAjrH18xAVhDFZO4sPigS9K6iki208hlcpenwXH1aw5VNMXJfQDfFBKM+pNPHwGgU7xgdlstpJEhfgZh3Sfpep16igiImXCEsxgbFoO84ZiRofL+GDMl4X8drQb+9QCUJCUtRsB71Pm4ecwojXeh9O9JgcalQCN4J0dT6RpssHQCjwpAqxzoDNUPSlqJhYYlmiZm65toh2Q7QbSCpDUJfZm09z4hBg6oBFJ+u4cAGvq8AQvMITE6gpZH3R4nmLGAprYSKaSv5ec5caleeVoVBa9oNAzQhKc+BLlPyY1BpSG5GMB4ysRekAY0akaUgYxChS0sKvPtT+8GHr08zMPu6Q/PO4fm6K2Y+TPPYKGUgh6fV6vPXWW1Sr1Qe2pPqkbMSPe46dnR3u3bv3sbDiT1ufxhLLGMNgMOA73/kO8/PzPP3005/4c/y0YqbX/wnm/n8j4mUPyihxYU93cOUz6MkavniM0vgaE+YIJlcollaJ2cD7BZjt4qNV8fOrnssp+vPCBKydI0jvMzSHKGgvotvBVXw6xccNcCmu/hS6cwlXPZWf2kNc6Til3R/SNo/QdguUo4y4KCQOVz6Gnm5idr5H1noWHewS7P4Q23gcFVQwvXdwleMoXcrnXEfQpkxjcpttvUwtblKfvEEnPEs4XacweYVJ+SzFrIsJCujpFi6aw9bOE278R7LFL6GyHi5ewAzexVaOy8xvdBMXL6JMRNJ4hsruJXCn0NMdbPNp9PAmqDDv6g7jwwZ6dAfSPnq6g6ucRCU7uNpjBFvfwVVP4KIWyiUyY9t9GR838YUVMRquP43JuujRLVzlEUzvDZkJlY8LsSZo4ErHMO0fovBkzafFPT8dYSunwRTQ41uS+VY8CM4RdF4jdgWyaBkfN8XM2Vtc6QQ+qIJPMJPblLKBxOqUjpCZOlkyQI/fwY4UUxWgggoqbggkaUyu2ZuirCVghsagVAGCAl5pvN6bi+WzMnJGo/yN94uklZ/lEONQ/lS55ZQJRVfmApyexxYkkgU3E7Fz2hatWlDDqwLeOzRTvE/wVMHMoeyOsEajRSlggRbihYpQzqOTNbyfI3P1nCpvRPSPFqjUT6UDzKYCPapQ/u3ZJ7N4FEpVhJ1IglIFojAgCvpQmsc5z2iyRWZjRoM+1sOMM/Q7PVotQ7Va/UyMmh+2mP1iZvYp1kdpx7z3zGYz3nvvPU6fPs2RI0ceuLv6tMXMWst0OuXevXs8+eST+4m5D7Ielp7vvd8PLjx79iwHDx58oM//4x2hvvdfYTb+uZxUXYZyCS5oyEYQLsnGF6/ikwFDv4DKHKXaCYyJIFMoZyHtCH3ajoSEENSAEFd9FDXr4FWByuwavnJBrJ1qT+SGvqkIroMWrvG+Tq1/FVs5ST88Q2l2G107Rawm4uwQeszO97Gtp6FaINh9Gdt6Glctoke3ccUDUDyImu7ioxoUllHTXYgauNJxyu0bEJyAxmPM9d8ia17AzXaoDl6jHZ0nGHcItcfMNlBxCz/3OYL13ydb+iWUm+BKhzB9KZa2fBI9WQMbodWUtjnGwqwDpoQe3hZGZNoTZt/oJj5ewlZOYCZr+KhFsP0d0vnPobMRWfMJ9HSbYPgq2dyzqGyIbV2EtEvQuYxVxzDDm/jSKrZxAT1ZwwUtcBlm5/u42lmJz7ETbO08mBjTfhXlLNnc0zLb0gYXr+JLx9FJG1KBI5Oppzy+hpl5fLyAKx3BY8UuSgX4wmFcUMbj0FmPIOsQqAQKVVw4T+YUNumjh9fRg2G+eecascIcymq8l1mUFC+HsjOB5EhQWYIkKcucDK1BG/yeniwo4IIyKlwSKFMh3++Fqq9nXQLXQadjvC7nxBExlFYqAzcRBqZp4vwYne5A0s4LWAvCCIWSuaEP0bN1XDgvwmYCXCZFV8+2sPGK/NxRgoRmfWxYyO2pBNb0qohSQk4R8bN0lVAS2ND38LqBoga2hzZ1UBUK0YhieQnrU+5N/1NGnRH37t3DOfcBs+RSqfRQiNLDzuh/VsGcP+v1J1rMPk47tmdJlSQJR44c+UC45oOsvS7vYTqjPVjROcfJkycfqpDBw1liJUnC5cuX6ff7NJtNDh069MCvu08A8R793m9jtv7f+Ggekp5Y7MSHRT9VPI4avI0vLGOHt5lMphhfoBR5tGmBHeGiJUmMLj2CSrbwhcOo4VV84Qhqcl3c1U0J5zSpOUA0WxePxd4b0sHZAb7yCKr3psCaUQtcSlY9C9vfx6uDzMJDNLQTU+Dem7jaWVz9MczW98haT2Mbj6OHt/HFA/hoHpUKGUEpjbcOsT5SeJvKz1A1KCdtKM4JgaN3GVs/hw+fZGH3FWZzL2GnPVzSIZttMSTGFJ+hufEHJPNfwCiNrZzC9K/hKkfxpcMw3UWnQ4o2xZUfQc3aKJ8KgaR8DFcsoyf3UbNdzHQHW5FikjUuEK5/DTv/ORTg40WywgGCrW9iW8+gp9u4sEky9yKl7ddBzaGnG+AcrnICZYUVaGuPYfpXRQbQuiiC5GyKbV6Ua234DmRjIbWM7wEeX1gSmDQbo2mTRAeJqkuQ9gjaL4PLcIUVXPmQOMCP7wjJQ8e4eAVUhCdFZ2NCYwmLZSgcxeuQxIYkaUaaTvGTGcbPsJMddCbxS0KrV/lMDAjiH+nL3k8GUVqQSOdQaiJsQEzekUmX5IlwTqFsgkoTlMlwuiQzvLCM8lN01kYlO+K5GDbxwSL4sdwQKsD7SFw9TCX3iVzNIVADbkKQ7pIgfpRKBSg3A9uRdHVTB2VQ6RgfhLnGUYNNZE6Xzw1RkRRvHQElYbQqkzuIiP+jowpuiIqfZWnuAksHZE8cDoe02212d3e5ceMGQRDsB5O2Wq0PEOE+aj3szOwXBJCHXGkqm85Ps6S6fPkyCwsLRFH00OaTwL5w8EGL2dra2r4SfTAYfKrW/0Ffv9vtcunSJWq1GsePH6fdbj/063o7wbzzV9Htr+OjJVQ2Bm/x8THxWCyeRM228fEKs8mEZDIlKC4RTtfI9CHi8Q186RF0/wq+egY1uSnU+rQn5I5kB185i+pfwZdPEk2uMfPL+KAsTiEx6P5VfHEFlazh6k9I7pfL8ON1RtMAX3icqttglIWQJaALuPpZ9Pb3cc2nsPPPofs3cIUD+GhBLLJUiEo7uMIy6CJ6vIarngDvUZN1XOkIgiF5IQaoEFd7VGZh5WNk8y8Sb32dbPFLUChTnKyT6YDUJuwUnqG19U26hccIw5CgeIpC/x3pBAtzWBWjR3f3iSI+KKMn26jhDYiXcMWDqOkWBDHh9vfI5j8nBI+FL2C6l4XmXj6Icinp4lcIum/KJukNxlt29SGiMJT5XWGFYOvbuMoxXGkFlQ5xpeP4sIRp/wDlHdncRdRsV8TU1bOAk0JoMzEnHq8TpG/h4zky5sEogfB0RNZ4Gq9jdNpDj+6gsrHQ80tNkQH03xYrJh3jTREfi2cjSqJPYjUijjzEAc5pBsOMzIdMpuAwBGFMGEaEcURggh8RGPfNGsV/UTwMJX1Z2bHEriiEkq8LYGJcUCWjRBbV0aFBuQHaDWG8JdqxsIEz86icPYkCp2K0S9Cz+/L+w2Wh5O/lknmBF120jDcLON0BqyAboRjgwwUImvJkWVe60KAu15/t4JURkT7kMgtRyYn9os6JLhFojfKJFEC/LVCkrpIWf23/flVKUa1WqVarHDlyBGst/X6fdrvN2toab7/9NqVSab+4NZvND0WbPs3M7BfF7AHXXsf0cZZUV65c2Y93efDX+B7eX9gnkXyS9X792h6seOnSpc8k0+zjlveeO3fu8M4773Dy5EmOHj3K2traQ5NHgmyHR8Z/D62G+OIxiQsxRVw4Ly7p8ar8GTQYDobYLKVYO0msJ/Syo8R+jK/kc7HySdTwLj5qontv44ur6P41fOkIatbF186jkg5p8QSl3lvAE6jRbWHtlUr5aERh2q9h6+dJRm36sznm9D2MDpgEB1C2KzZV3Uu48gnc/Evo3hVc6RCudAiVTfGmIFEu8SrEi5jeFYHaSocwuz/ANi9A8QCm8wYZh3FBTDDZwJUOo7zHlQ6hJxsSsrn0SwRb38C2nsEXDxCM1zBRg4LLyGq/RHPrWwz1aSazKX13kEb/Ln46whcXmZgFSm6KHtzAlw7giqvo6RZq1kHtdWRpn6z5FMH672MXv4iy05y5OCDY+SHZ3DOYyQa29ijYMWbwHrZ8nGZ6BeXPYSsn0EkHWxcBerDxDWzrabwOUNkE23wa8Jju2wC42iPogYSOusIKxAKNYcrY4gGUHVMbvCb3nD6Ni+dQaR/FAHQkszMT5fOvPsqlONPAhzUICmBn6PGWQHfvM8v1cUtmhKaIdRHlapWKdth0jJvt4JIpdiDuHEZ7tFYoE6B0jDeRFBlTwJkCqBYqWsyNd8mdMhKUG6OzIUXfJkhGKNUQ82MdocIie7ClVyFQQaVb6Nk6Pmzgw3mIj+QOIUJCUekW2oZi0BwfQmBCh7FtAl/GB8u5QNzLPDlaFhG0iiDbBVMWaFIHqHQHH7bwqiAHRW1ACVvTqyLKj1G+CIiZsfMFQjXFmSfxwYeHURpj9osWyOG/2+3Sbre5ceMGk8mEarW6X9zq9foH2NO/mJn9Ma7366A+zJLq01DrvT+KVv87lpbqWHv2Y79/D1YMw/AD+rXPIm364x6fZRlvvvkmnU6Hixcv7l/ADztvU93vMb/+f2bqd3HxYfR0B28CvIrFkDYSf0KriwwGI2JGlGonCZLb+MJRCtm7YjQ83cKHNYFKiiuyh5UOyd4RVFCzbZm/pQN83ERnUwbBcebSAb54CNO5hKs/JinGhRW8LjLbfZfExcxFDtW4AOP7mLSDtVNIBrjmRXT7NXy8hKudRc12UdrIaVkXcIWDmM5r2Op5bO08wfb3sM2nsM0LBNvfIWtexDUeY27z28xKF3GlI5jeVVz9DBDigho6G4FNyRa/TLD5bWzjUVzpiJgBhw2C8TrZ0hep7L6CrZzEO8vMP0owvE6WzNCqQt81ZXMd3UeHFWy8hE46oDThzsuk88+h7Yhs8SsE29/D1U6ASiCski18HtN+FVc7hR68hy+uCKllvMaYBRrD2ygybOMJlJ0IRX/hJYLOG6i0T7bwHCrpgI6xjSfBTtGT++ADyYnbfRXCMq58HFdsSFKAChkUzmLCMiXbxnReF4ixehII0KPboJx0xlETH89JQbETsDMA6cyKKzhdyL0UHcolUgCzERFDdOZQ2hAooFTF+xoesM6RZI7UWmzi0EFAqEICExIojXYZMENlGVKYpNjJTK0EPiJzYyIVCKXfu5yaH6GyLnpyTwTcxRV8uCQdlU+FpahApx1UsomLD+OiwzktXqHsTCKH4sOkegmcBZeh03WJsAmX8k5sF+eLAjfqQGKFTF0c+72X4qdLCGSZgnb5z6ggmjJdQGDHLaBGWnywmJcwDFlYWNgfd0yn0/2Z+v3798myjEajQavVYjqdPnBR8t4zGo2oVqsP9Lifh/UnXsz21p4A+eDBgz9hSRUEAZPJ5CGfeRnn/zMW5/9zKqV3Uf5/jOfPCQvpx9a9e/d4++23f8LfED69Vu3jYMbBYMBrr71GsVjkhRde+AAu/sDFzHv0vd9Fb/13ODcl9QUx1Q1q4Dw6uYcvHkWNb5H4MqPBiFKQEtZOS5ErHEKN72BVBZPuonSI90DahWgpT4deEZpytCxEEFNGTdbAOkyyQZTGYqzqLK7xBGq8ji/MoTo/pOOPoFWNSr2Jydqo3dewzcfBdUh0TGW6CUkP17yIGt2GyW6ugQMfLwurr3wM27xIsPNdstoZssXPE+x8j6z6CNnCF+XvtVO04yeY772GbTyObZzHbP8A13ocFdTws7aMaibbZAsvYXZ/gCsdEH3Z5D4+qGJ618lazxD0ruAKy5R8Hzf/OEH/JkwGBNYxoE6QdDCzIYXhJkn1NJHKyJoXCO//PtnyV1DpgGzhc+jhHXTaxZUPo9QIO/8cangHVCA09vF90sop7GgNH5XwUY1g/Q9wtVO40io6G2GrZ8AEmO6b4BW2cQrdvw5xQxxL3DRPyT6EjxuY7pu53u8YrriKcgOMHUKhhS0dFvLHTPLPsAm+sIzXIXqyhZ6uS4dkYlxxGcImzkh2nU53EaGzFvsppfCmQOIthaCFMlFOpwepiB7jQStPDHhnSZIZaTJjNp3iSQkNRIEjUCnGeGFk+lh0Z0EJZ6rMfELRFMD20ckWymXYwhI+rOOLNXH9QOd9mkanu6jkPq5wCBcdRHkpYOLQsSvBmdEihDnj0k4JXQ9PHRcuAxpsG+/LP7KkyjoCxe4VtXRLCp4uoexQUiVUkBc02Wa9ilDMwMc4H5D5ZYLo3INuJR9YhUKBlZUVVlZW9gtRp9Oh0+mwu7tLu91mMpl8IHn749YvdGYPubIs46233mJra+tDBcifXvR8kvWN/ynVyr9BqX+Jcv8O3Jdw+ldAlfbfw/b29oeyFT9t2vRHdXZ7s7mjR49y8uTJn2AuPdBrT+5gbv5d9OianGp9QNHdw4enUGkfyPDFE5DsMrRNJpMJtXKNsDQvM7DSUVQ6xBdXcdlQrIsK89JVlU6hxndwxcMyA6s8InOyyhnU5D6ueBCdDshKpzHJO+AD9Og9YdTF86RJxtCuUrO30POPo8f38eWjQt/v3wTTIMq6+OZZ1PAmqvsWvnYSlU3wOkQNb0PQFP/E9qu4wrKIlDuXccmUbO55TO9tXDYjm/8cpvsWcRoyabxAsf86rngQu/A5gq3vYuun8fE8TDYgFAF1NneRoPum+DKWjwjzMl4gaL9B1nwcM7iBD+vowXukpSPYyXuUoojCbIu0dRw77THNqpR2X2YnfJRCMEY3v0Bl67u45uOoyQ6udBBYwXSu4OqnMd2r2OpJvJuJkXJhlWjrWxh9CBctoP2MbOEl9HSTYP0b2AWZveHCvBubCf1fxXinMLs/EIZi+bBQ1u0MVz6Ji6ro6QbBzncpZ46kIiJwPbwJQRFvyrjyUs5gHEkXHlSxtSYurKK8FZZm/xrapwiV3uOjlui7giJSICzGTjCTDbSbirmu3zMbzgtb7ozvTUBRRRTCGAoFMlUmzWCcedLEojTEoSYKHJEeo5M2ys8oOAVuNXcAmZPipZQgPCrEO9DJPRQKVzyEi4+g/Dh/f0A2QrsNibqJDuYOI5L0rNwYq8p4rYkgL1oNvGnJSMT2hQVp6oAWeDGaxwdzAmGiZJ5oE7wxQICyieTzkYGPgSkexSj4KvUH2EM+bimlqFQqVCoVDh06xOuvv06xWCQMQzY2NnjnnXeI45hWq0Wr1aLRaPxUidN4PP7FzOxBl/eeH/zgBwAfaUn1WTh4TKaPMhiVKZX+O2CC5/+Lzr7GNHmcH14+hdLLH/seHnZuBz+9IL3fSeSpp55ifn7+Qx/7sZ2Zd+j1f4Je/+dgB/hgHpVsEtgZfZYpZyOZL5gqpF16I1DZkFYlQscNcfOIlqTAmBicI7RdUjMHsy1cvCwJzaWjYtRaPyd0+PIjqOFNfHEF076Eq53BTO/R1yuU8Nja4+jBVSazFn50l2L5EKb8hBTMwgJ652Vc6yl8McQnqWxEO69i5y6gky5qsg0mgmyGq5xCd6+g0h5Z6xnM4B1U/wa28Ziw9kb3sNVH0NMtGN7H1s6gd64TjO5i5y5iulfx2Zhs4UUphsUlfHEVNb6PjxqY0T0x8B2+h84hSTVr48pHCba/j51/Fj1Zx8dzhN036aoVqjrCFQpEu6+RzV0gcgm++iJL619nWHgWN95lU5+l2r6NMRFqNsYU57BzF9GD67h4CbP7Q7GwKh1GJV3SxpMUd98m2LmPXXgWlY1kvrd8BNN9Q5iKzcfR/Zv4uCE2YdlQfj/lo+A9webX8WET2zgLyqLTIQQ10rkXGPTblNM2OluXayJegKSHGVwDUxRn+cKisAhtIo9VCkxB4NaggFIBeI/3M4EYM/EaBHLGYh6YqUA8GMXGyuc6s313fISBCpbQJ4Q6oRSmoBNSYlIXMZlqBtYQmApRWCIjQe1ZtKlQtGnTjTwQU967K57KU7G9ONO7FJ1sydwrWgRfzkdsmTBzo0V8sCAFaZoS0AdflRkZRrotlOTTgcx2TTU3WvZgB0IKAbB9CKr75sEolbMZQ7z2QJk0C8jCpx5sE3nA5ZyjUqmwurrKsWPHyLKMbrdLp9Ph1q1b+6zFvXlbtVpFKcV0Ov2ZFLPd3V0+//nP8+/+3b/bj3e5cuUKf+Wv/BXee+89fuM3foO/83f+zkMbW/yJE0Aee+wxisXiR36AIAg+VSEBKUaj8TPieaf+W/CG8aTLsPdvePxUlUr5SXyg8TzzUx//aTuzHy9Ie7lnxpiPdRL5uGKmej9A3/uH6MktcVMImqjZfbypYsM5gvE6PlgB73HjNbqjgJIeUCxHEDZRo/fEDX98N3c3D1HTLVI9T5zcheIjQvgoHRLCR2ERNbovui47w5eOyJyicgqVdEHFVJKbeE6jxmt0/SpM25TmzhMP3sQlYc6OK+KaT6K61/C1U5hkg8Q08ZU5zPYPca3zAhfpgqQVT7ax9fOY0W3RYtXPoWdt9OAOrrSEymZSfMIayjnUtMPMNAhDjR7ewVZPoScbmM6bZM2nCbpv4ZMxrnoCNVrDx3X06A6ufFS+b/c1bPNJIcg0zhNs/BHZ0kuoWZescoK5nR/igxdQdkrWfJJg41vy/7MZ2ep/j8rmd7CtxylPOyTRabJpFzO5z2RmidQaafkYhWRIUDyEmvXQg5vY+YuQDhiZRYLWMuHGt3DVoyKunu0KUQSPHr4ntG/vMbuv4Uqr4vJvR3kq9rOAI9h+GXyKbTyODyLMeJ3AWrJ4CV1uCmswGwgxpnAIH9VR6RDdfl0o6Urh4ha+tIo3RfE+nGyhfJqLoIWK7nUkUKQOSbzDhnNCPvCAFmmILI/Ci/EvHpQXWyjv8cpKQKVPUIQEJiDQIUUVYFWB1DrSNMH7Dkn/NoF2YApC9ikeeV9MjAW0FLB0Bxc2RY5iisImdFagWNfBxas5lOhl7pt18L6MC5rg8+wxpfBBRYqiHYEOBEZES3p1uACmjrJdXNBE6VpOqqqJJAErH1WleB+gVMbd0f+A1c9AGP1R68cJIEEQMD8/v39oTpKEdrtNp9Ph7bff5td//dc5ePAgBw4c4J133uHAgQMPRSD5aWtnZ4evfvWr3L59e/9rs9mMr371q/zyL/8yv/d7v8df+2t/jX/8j/8xv/7rv/5Qr/EnDjNWKpWP7To+K6Ng5xyeP0vmegw6/5TZLKXRnCMOQpS7hkr+7zCr4IIv4MP/EejmZ/Ye3g8zbmxs8Oabb35oZM2Prw8tZqPrmLV/hB5cFgaVaUCyKyf5+IBAUG5I6ouQDkinXbrTMo2wR1hqiuYl2cWXTqDSrpzQVYyyI1zlNKZ3j2l4hMiO8eUjQgAIm/lJdyYi6MkmPl6Sbi1eFLiKgKlJiZIp00Gf2G0RNY+jswG29TR6vI4Pm8JSrJzA105LjlY0T314GVd/DtU4g5rsQlhGDddw1WOo8X2C7VewcxdQYV8iVUoHUToWvRmIFMArcWgwsVga+RgftVDTLXGf1yWC3dewrcfRwzuY3cvYuSfy99UQAXT5EErHmO2XsfMXUdmUbO5ZgrU/IFv5CioZshs8wtL6H5EtfR7lE7KlLxGsf51s6QX0dJds6UV0522I6sTTe/jyIXx1nmhwi5leotx7jU54Eu8tRR2gi6co3/saWfMxPEZSsJe+gJqsE+xexs4/iR7dFaZi7VHIhqjprkgQ0j5B71vC+qwcQqUDALLWRTDiSqIHN/BhFeebxLMtgnQdH1Zw8QIujoUEYWegA1ztFD6oCHXdjtGzbdG5uVSutbCOj6tgYrGJI4VZF52NqNs2Uff2PmtQ8rpET+Z1ILrA/M+9/7yOQRdkNqo0HiciaDdETTelayPDxfPs+ADTOEuWTXHpiHTYx46mhEFA0QwI9AzieVzYRJkyyo3xNssh1A4uMmBauR2WFbuqbICPl0HXpRi6KbhQ5CXeiRQEK6bABJC1ZX4YzItHpArwpp4nc4d4UxFdZSDJ1D6PsAGP1/N0po9y6DMqFB+2Pk40HUURy8vLLC8v45zjX//rf82//Jf/kt/93d/lL/yFv4Bzji9/+ct89atf5S/+xb/4qd7Lb/zGb/Arv/IrvPzyy/tf+w//4T/Q7/f5e3/v71Eqlfhbf+tv8Vf/6l/901vMPklL+VkVsyzLGAwGXLp0hMMHn+DIgffQSgvKoTVYC3TRs38Ds3+D18fxwRfx8Zc/EzbjHuV/bW2N8+fPs7y8/Inf+wdee/gmZv2foPrfQxGKL53d09FUcXpe0n9ROFOl4N9hPC4zSSq0SimmcCh3KpjhCgfRSUd0Mh7IurhoQXRaqoxJevjiHFhQBELRthMJ20w7+NoZ1OgOvnAA3XsLVztNMLqOdXMMBkN04QClaCb06rQnXoylw+JL2HwK3X0z34yHeFWjH55irn0Z1zgrp31dQEUNEU3PXQRdwnTfwtYegUIgRSyP9iCso2Y74DyuuISebBK4iZjEZmN5rmQg0oTqCUz7TWzjHMoUCTa/R7b4vOjtwoZ0e+WD2PqjBJsvYxcuShba8pcI1n6fZOlLBL6XF7A/JFt+CZUNSA/8MsHW93DNs+jue/tQpWKGGt1FmRKudop4ug1zT7Cw+xpZcZWJmSOdjtgKH6Pc36CVtZmVnyFOtyBukS6vYgY3ZRYTtQSaLB3CVw7vf6Zs7mnUdIfg/tfxxQVs7TQq64HV+MKKMBazIWFvDU2KK6yCMULrt2MIirjyIXzcFOgu6cn9qbTMhUxRNmpFnqY8E/HyXhZZTq+fzEKCUhMVhOwnSO/d5opcDO1zlmEKNkVnE5nxOXEK8WFVgljDMr5UA5yEhOLQvofRijAuooIMlXSwPmCmmwyzJs6OCKcDdAhhFBKpIZgU4gW8mkfbBK8ieW03wQVVNHmRJkWR5YzEPDDTz8BUAA92jDcFVFAFfJ41V8qJI/3cDcdKATTl3CWnhPIu96D0pJVfw9rsM7Gs+qj1IKJprTXnzp0jDEP+wT/4B/upJF/72tfY3Nz81O/ld37ndzh27Bh//a//9f2vvfHGGzzzzDP70VWPPfYYV69efejX+BMvZp9kfdp5Fcgvq9frcevWLY4ePcrho7+N9v8PlPuBQB0+d+12oJQFZ1D2Oiq7iRr/N7TMCpPgKLgz4sn2gMs5x9bWFlEU8fzzzz8QW0gpJTf61v8H3f73qOEVgWrMvPhdpDso72SYnQ1kSK3LkI3R07tMfYMo07RqIcRLkAxRpDjdEBp6UId0jMq6+MIRdP8dfPEA4WgN54FsJpt86QhqeB1fOSnEjtJR1HRb2H9pH9d4HDXZYmhWqUzexVdPU8zu4sPTkglWPo6erEnHRQqzPrb+mESkFJaIdn7I2C3jFp5ETXfwUR3dvYqrncE3HyPYepl07klxw5h1ISiisimusIC2HRjcFJr7ZBPTe5usfh7GNwhGt/GtM+jpLt4loIUp6qrHhYBROylF6/4fkq18QRIEwjp6eAdXXiWbe5Jg6wfY+SdR6YRs5ZeJ1r+Ojc4KS3H1lwk2v4OdexIzWsMufA7dexeiBqZ9BVt/REgu4w1QAWbrFez8M5KD1nwMlfap9l4jW34R0gGJPcr2aJlW+zIj3UKFIwITYMuHCUwmP/PiEVTSx/TewdZPSTJ0NoCgRrb0Rck5a18S95DWOUh66OkmBGWmegFfKFI0qfhrFlfwYV2aqOk6un8d5a2kS1eO4KMq4FCTDXQ2yn0WJcXZBwUwJZmv6QAHJFgIK0jgppPC6FyuXxdDXkma3uvO8mmb8tL5kcmcSQm93WsjRRQgaVPyWwTjES6aF/g1bKLtkKJPKRQLeCL8ZIPU9RhNawxsRNGMUElAEIVEaga+gje1nEzj8pgXh1JF8P1c9JyAyu91l4lkQcUoAsi6EDTwqoqyHZEA6DrYHpiadHcevC6KrMIUUWT44CCu+CLO/eEfSzF7UJhwOBxSLpcJgoCLFy9y8eLFz+S9HDt27Ce+1u/3P+DqtJcb2el09mVJD7L+VBSzBxE8/7SVZdk+RfXChQv7mLHjf4Pmt1HqzbxDtILfEyKnKy1YPhCpGyyU3iTY/RbeHMAH53Dx0xA9mVvtfPja3t5mfX2dYrHI5z73uU9+gdkRqvstSjt/yEXzHzH36iilcUEemuhG4Cw+nEdlE1TaEahGxejZOknmaI+rRL5PvbaID+tCv1Yap6voyU18vCKQlJvhS8dQkw0pWtkYF1RJbEjRpcJcHK/hKifRwzv4wiK69w4UFlG9a3Lqnd2nNwux6ZBpcISFwOELR9G7b+Iap9H9d3HVU+hsIG7k/evo/i18cQ6VTkjqFyjtXIKkIq4PzuPqp9FbL+NaT2LnLmBGa/jSssx4iMCUMN23yern0Cog2Pwu2eJzKB0RbnyHXnyGKEyJtl7BLjyDSjqo4V1c5Zj4UpYPyXuoHCRbeI7g7h+QHfjyvnu9Hqzhi0vYhYvo3ddxjTOoWY9k6Us0738L6hfRk03SpRcJ2pdxlaOYztvYxmlJI4hamM5VXGkFWz6Eme1im+cJ1r6GXXwehYawQbb8EsHGt3H1k4QqJHJTWHmJ4ngDNVpjpA8Qb73KKGxhiysUfEKkYlzrafToBmbnDVzzLC5u5tqzCDv3jMyNJmuopI8rHQCvqU2uorICqriEKy0BiJhegQ/ncMVVKfg+FUH1dFuKjEuFjh41RfuFE/3ZrIPOBig7xuBppClBt8A+tGiMEDW0FhhYmbwgBqB13oGH+SyqCHl6tEq66KwNODwhrriMDVsMMMRxGaVm+QyrKKnRaV/gwWgRVT5MwXYoEGB1FTtzpNmY/kzEytpsEcRVIm1RgRZCi0vEH9KJS77C472YHwuBJQQ/Bh/KgdYl8nVd3+9svaqJ5VtQk85vzx3EW7wOSMv/M7yXw/NnNY/60O3jUxSzP44VBMFPZC3GcbwvJXjg5/us3tjDrgeBGR8mwkVgRfFWXFxc/CBjUCmc+evo7G+Beg+lDcq+L19pT/hIIP5rXskcO1tDZZuY8e/LiS04gA8OgzmJi45DdEp837zn+vXr3Lp1i/n5eYIg+PCLyzuY3kFNrqLGb6PHV2F6S3RhLsURykws66P9Ll4VcKYOboSebUn2UziHStoo22aQlJiNBzTKnv6ohFdhHgPSklnabEO0ZrMuXhfw8SI67eOLq5AMRdejjUSPFA4LFFk8ICzE0iGBu8o5XBnPkVlPMmijdYlKmDCYJHiasi81z6DSCb6wiNl5Ddd4FDVex9XOoHNYkOkmxoe0o2MseIcPq+juO7jyIdziC+jOFWzpEC5uoexeptdVETpXjhNufJts8Vls60mC+98kW/wcdu5JWhvfZTL/HEHzPMH9r5MufQFdCDG7b+DmnpDPEc+hxlsQz5Otfolg7Q/Jlj8PQRmPxow2cIU5bOspTPdtXOUQerTOduE8S7338NUjmO51bPMJKZTxImbrh9i5x/EmE0JbMiAY3ce2zqOyEdny5zE7lyEsYmvHJZ16+Qvo4R1hX+qDBP0b+PIqrrRIdbyODw9jnEUPLjGMDtH3JeLpNqFpouaOU5itEXTfwVUO40oL6P4tiMo5HBmgZz2UHTM1C+jiAgU/Itj4jlx+hZZ0YSZCJX2U70iQpjb4eAVnIoEInUPnuWa5ah6C6n6+mcXQ6/Zp1RekUO/dryonfHiP3zMNtlNUOpBZnZshB0jJ0nNRCx8vYovLcnDzU5TP0FmebK0UpFMJ1Qxq+KiJM4dQWVfmv2EVT4RyE1RQJSzOESc7lKIy1hbI0hHTxJHaPnacEYQxUegI40AKj1I5SSWf9zmPmP0bPF6gSBWgMMKAVLHE0pgAdFW0a6aci91LKOdw0QFc8XlsjjL9LDuzvTitBy1mexqzh2UUPshqNpu89dZbH/jacDh8aOvCP/Fi9kmWMWb/NPNJf8jee+7du8fVq1c5evQoxhj6/f5PfqMKcMF/icr+Jp77KO3zeZIRdwFjxDoOJUNpZcCmP7pJvUelWxLtwcsYlwrk50N2u5ZaUuArp44wGjsmM4fZWME7t2/PQ9aDbIBK2zk0IadCTwy6JpuAGxDSzSGMAk5VUekIle4CWsSadoxOdrCE9MYxJmvTqLdQYYNgcB01s/jCKmq2BSrCFY9IcGNQBDRqIjEoerSWD+nLhNM1hmoxhx1XUcNbEoORTVFuJllbdsDUVZgMtglKx6hGKamuEI6vgFpB96+LQa9LIazhGqdlxqOLmJ1Xca2cpl89heq8Q3G2jq8dhyzFNR9Db/8AXzqIqz8qUoCgghrdwxcP5POs75PNP0W2+Dkhh7QeI1t6EbP9Grb5KL3ykzTar+PmniBbfIlw/Y/IFp/DNc9hNr5PtvRsPnNLJTHblchWf4ng/tfJFp9FBSVscQkz2cRnCbZ5Tjq5sEY1uY9deRwzuI2P5+Q1559EJV1c5TBm53Vc7Tg+boEa4grzUihXvoRKx9jmebAjgvXvkS2/gB6t40oruMIK5e038cEhVP82Rhlc/SRkE0kDX3iG6vA96sP3mDbOM7MK199k7GNU8QlKbkDceRfCMl6XMJ23xaqqsIArrJBMtin5FMIS2dxT0iVnI/TgDtpOpEMprUA8B4CebOS+j4F0T8pAWMEFZWET6vdtmDZFK4vKxnnStJV5Zs5T9yiUDvJYmLIwT8n1Zz4TliRe5nB2hGdPv6ZRyRBth8QOoImPV/B+hs56MOvgwxpexT+i5AcVSKboZDvXglUAhQkKhLZLXGwAK6TWk2YJs0mX/ijFaPDTGYF3mEIBhRFqvRZNlsLjVUG8LY0Rtq2fSEFzWU5oKQuzUhfBTvBBkawibh978++fdTF7mO7vj9PK6umnn+b3fu/39v99+/ZtZrPZJ86p/PH1swVtP6O1Z6T5SedmWZZx+fJl3n33XS5cuMCpU6c+GqpUMT74TdALkJ8mvfKgFcorlBJrHik0Sro05QCzn8/nNYg3uCdNLTu7bUI9ZXnOEdlbxO4qJf8G9L+LGn4fNb4E03dQybZAfLqcx1bUAC0n0awtA2RdZOYqEqmR9tFpW1hkpiUnxqwLyjDzFUadDSKGVOeOYkxROjBCYV3NdsWINaijZ23xkUsnqMk6RE1JPdYR6DJqtk0aHSZOd/IiOBQmlymh0r441g9vM5pF+M4VipU5qu7+/nMP9AGUt7jmExLSGVTRnbfET1YLkcRVT6J670l4b/ddssoJMl2VE+50W1iMC88KnDPpkjmwSSIhmO3LkI6kcLXflpTnxefQw3uodIidfwoz2kBlUyaNJzGDW9L9rHyJYPd1yGZkS58juP9teU9hU96HzVDjXbLVrxBsX4J0AqaILR2AdITu3sRVj4FLSVWJYPcNXPVwLk04jNn8nhT8oIKrHEWNNjDd93LhMWQrXyZY+yMxPk5HKF0iW/0ypv22dOHD++hZm15wRGAtFeGLiwT3/0hmfoV52VgLq6SrXySebVIfvEGtUqVRjqj4LokN2eYw7aTErLdJ4gtkxQOoWY9g/Y+oTa/n3W01N9ntCkGhcgw79zTZwvO4wjzYMSrp4x24aBFbPoYtn5CsNl1AJT10/zqm82b+3xXM4B3K6Yb8HnKfSuwYZeWQt3cYVUoYkNrO9u8rdCSQnEOkCqO76OF7Il7H4EqHyIoncLqInnUg6wMap2Pp1rzLgzND9GQTsqnMg5VAnt4ruQc8+KiJGDt7IjWhVKpTrS/RajUIVIr3MByndHe36Pd7jGcpmc3fp3fCUNQRIJ8LXQYS6Wb9TAguBNLdqRAfHMAVnwPY34d+lsXsYV/jj9Mx/6WXXqLX6/FP/+k/BeDv//2/z5e//OWHhl//xDuzT9Jpvd848+NWv9/n0qVLFAoFXnzxxX1bqI9lRKoKPvxNcP8lSrXzYXXufo3OERYNeDmZ7hmsKv0+BMUxGk8YjqZUSnWKhbLQcV2GJkH7CYo4H4pLBygsLZ3/OxYHblXJHYASgQTpE6kxnroYprpEZhxuBqaJJyQZrjOb9AgKyxRLVZlLuQwfLaH9dVQ2Elp6MkC5vBiN7stnKBySDaOwIoN9O8OXT6CHW0yCeYpe4aOKGKbaIb5yEp906fgDmGmbeO4xwmQXX1hB997BxgvU0pt4zsJ4A185jkqGUtj67+IrR9Gdt7D1M1A+AGh81CDceY2Ug7JRVE6g+u+idt/CNR9h2t9hPLOUkhuMTR2K56j13vnRPGtwSyDNyjEhh3iDK69gOjvodIyrnUBNdsBZsoXPYdpv4orLAiuufwvbOo8vLMJ4A8IyenifdOXzBJsv4ypHIKrm8OIGun2NrH4SN1jDFZYwmz/Azj8lDM3aKcz2a7j6CaF1l1bxPiO8/12y1ReloB74Irp3HZWMcPWjkm+2cAE92UKNe/hijeb0XXzjiZyt2CNrPYWadQju/iF2/kl8WEAnA2ztBLTOo3vvEUy30fVThG5GLWmTmRoTvcw4HaM6OwRaoUtnmaWW2myXYHhdinDtOC5ugZ2gJxt5ZxFCWMHGRZlt+Zy96Kb5/RJA2MBHDQnENCEojXXQt13C+jxy8MvNf9nTmmX7kTUCMY5AyX3pdZRDjE0oHAStc8bkWMJI7RSvIqwXRqXKpuLLaGp479GT+/h4QQpaqARFIRBPylxOQIgcRlNxJ/GR6MlwFmW76GgJS4lSHBEFGqsKJFmGSzr0phalHVHgCeIaYaQxRiPwqMKrkjAfdQHvJ6BKMmMzZdLaj1Kkf1rc1We99va6h4EZ99iFP+sVBAG/8zu/w1/6S3+Jv/E3/gbOOf79v//3D/98n+F7+5mtPZbLRxWj98OKx44d48SJEx+4WD4RvV818dH/ETX7TVBdGV4rn58oTX7K8nIjp0kOjZg8ZNbT6/Vw2YxWvUUYFPIcMSdZV8rlLRyiIUIjLYERJhUO/FQKo0MGxypCBVW8czhGovdxQ7yu4oIG2AkqGzAeT5kkmlrtMLGa4e0Ip2soP0Inm2QUsWFdCo7XYJoC1UWNHxWowgpkY5Sd4oIGarwGqkiQtlHJFBe20NPbuPIR6F2nk5Qp+BHFxjLKzsQaynt8+TA4z0w3KM76svn1b+HDCqQzfO0UJENc/VFM+4rM00b38ZVD2FpEobOGZwXVvYarn0ZNtphuXidRMY1iEZpPUWi/QTpdox2cIB6uo0bXoTRPbC1apznspZEhfh55770UFxRq2sE2HkUP7+YC589jNl7GVQ7jS6uo0To+rmF6t7ALz8l8zWaouIYrraAn2wS7b2KVxNy46nGh7889DrqIrZ9Gj+6jlcJWDqOUIVt5kWDtj8iWn0ePtvPuLpOi2jpHsPs2tn4M32ihhvcZBivM7b6ZEzkek8NLXCdd/SJB5ypqvIldegaVDKUolg9B7bgImpMhvrCEsQn1wSV8WCGrHydxIXbaQdmUPlV0YYUwDIkZEQzvCunFxPhSSw41412C6Xo+NhLCho9q+KguZAdtyAdpEt3iElQ2o2S7mEFfMr7ylOh9okcQ5wWovN8dyU0hCdOQCU1fSUfsdYBXgcCgLkMpi1MxPmyhsl306C4+nsMHZXyUJ3Dk7iR6fA9bOICLFxFLLS1F0Vt82ABSKWJZWyDLoAXeEfghqAZKxwRuhInLUFik7C2phSxLSGYDhiOFCRRRGBBGIUEUo3QosKrO2YuqiA8O4AsX9reZhw3NfJD104KOP8n6WVtZjUajD/z7z/7ZP8vly5f54Q9/yHPPPffQeZHwp6SYwUe7gLzfbf7ChQvMzc39xPd8Yq2aXsRFfwM9+z+h1FC+ppR0asrjnZZuy+T6NKVJkxmd7pDIaJr1JsrEQiN27M8APAHWOaHqeiW2Ps7vz5eVy2nLzqFUIm4EbihQCBpHjDN1NBZlp2BHWBfQ6YPB0Ko4tJ7gTAvlUnSyKam90SqaW+ikjYvnJYE43cYXD0oxdBN80EBNNuUzBs3cwX1VIC83w4crcuotHca1r9FLS1RMn6hclvlXOpBOL9kWvVnaI1FlYb6Fi+jZrtzck7sivNaBFOjWEzIHK62it18jq58j1WWBbOIMvf49dsPjhKZKrdZEjTeh+y5u7kmi4W3m0h2yuePY6YA0nTJORlgVY6IKJbuGKiySBi0K042cpFNBT7clASAdS2FK+ujODezSc5idN/DZFFc9sm+MrDtvk82dw3RvyDwkrOCKS0BArXsb3Fm8KZI1HsW0r+HLKwKhVg6isinB1g/JFp9GpRPSg79EsPUavriAHm3g4ybZwrOYwXu4eB7TeQcfVEirR2FyF1c+gg+KBHf+ANc6jSstopMhtnocmmfRnavCUmydRQ/vys+1uIQrLqPSHriMrH4Owpige5Vw1sNHdTp6mTguYLIe6UQxsGCDFmFUJAogdjMRQQcxvnJUNF86QikH2QSVjQQG9nv304+E0RryTK8SKqzkh7I8hVrnQZ1KCdMvTcSqTAe5L0gAzuZpBhMIyuL6H9YhqODtGD3dpZgOwBaFEBXtadkClApR0/sS+RI1xc9TGbAWPV3HlQ/gotz71c6kiBVW9y2pVLorSdxUKZDIwS+oyJzPjiGoEGpPECgKpox3GanTpMmE4WiCG/YJopgoMIRxiSAAwpC0/j//wBaz15n9LNefppTp1dVVVldXP/Xz/IkXs096cviwYrQHK/40t/lP8vif/s0HcfH/HjP9O3g9lqKkzZ4Bj3A/vAEyxtOUYX+XUqlBuVjKZwM5opJrTSDEK43zKXhx896Lr8jbuxzS1HglJ1FAdC8uhWxEgKQME1VwQYNkMmQ8WKcUlimVy+K5aKeSXeWspEJnE8i6Mm/QNcLJujh0RKsiqlYabyro0R0RQxOIW3z5CGraBlNlZmqU3RRXPcm0s87YNqhWikSRkeF20hNIcHIfXxZo0JWPUktfx+snMIObuMoxdNLH188K9T+soXvv4OMlfBCBdbi5pwi617G+hurfYBYfZqRWqWbbhM0jeT7YYdR4XWC9hadQyQAz62GCgCgo4WsL0L1Jaj0DtUSxfQOjKwxKB6j1bqPKC7jiCnpwSxz8ncOZEiqO0e1r2OZ5dP8GpnMV2zyDHm/jywcJtt/Azj+GGt4Tpl82JYvnGJsJzd5NfGkRH9Vw9VOoyTZm0sZWD+ODMtnSswT3v4NdeQ4z3BCCyGQbPdnBqwgz3sHVT0hRCpsQlojWv4UPjuOjCsompAe+gBndJ7j3LezSRVQ6hGyCq58CNGp8D7IEX1lEt6+B8rjKIXxhQSJzbIqrHMe3KpBOKO5eI04SVFgmqh4VYtNoDTu2ZD5gQIyLakJdDw2ht2g7+tHFH1SELZjT6aWYiGt+mmWMsh7F8lyu3dy7a3K7KJfkBXEoujgl8KIykRSgPbE0Dm1HqEx+xy6qQVDGmgbO2JyEEYApoKb3Ie3iiyv4wkGZ1XqFzsbgdvGFg8LSJZD5XTaQKKJwTg6PyU6eXL6A8hmBGwF1kREkuxDNiwA66+MC+TouQZmQ2DjiqA7aYR0k6YQkc4z7eWhndJy+b9Bqjfdt+x42AfpB1sNmmf1pTZmGn4Ni9knXjxcj7z13797l2rVrHD9+nOPHj39kYXxgFxFzDBv/dfT0/wJqilIZ5GJPj8a7lP5gyGw6o1FfIN67cPLxF3sO3Si8MgIqegXKyYnWZQIvKicd2o/Pz1yQa3EifFjAkuEIMdmI6bjDZDqlWFmlEBch7aDttpBIgjoq6aOTXbwp43Wd0G/loueDIr7O+uLmkE5Q03ti45ONpEsrH0XNeviogptlBG4Xa44w2bpOSoFGKcKoGd43UNMdXGFJyCSlg5D08fXTqGmXQXCIhdEmvriE2bmMazyC6lzFNU6hkoF4Mg5vAWVhPJYOYCtH0btbjM0y4darFOceJ4xyvUlQxmz9gGzuApgyuntduh/jxXNvso2adXDNR4h714mzDbKVp2HrTeLRe+xGR6h076L722T1UxSH99BxRdwu7ARfWsV0rmGbp1DDDczma9jFC6hJG1c7jtn4AXbxKZi2IZtiBncFvq0eRU+3UbMBrrSELy2DnRLsvImdPy8zugNfwWz9ANc4ge68i6sdxUZNMQour2Lufxe38AS+uIDKhiTzF6mvv4rZvo9dfAqdDnHxAvbgEUz3Gmraxc0/JtT7MKfe44RFWZjDF+bRo7vSaRaa2OYZgfGmXdCGUXQQX20RGYuedXILqxhVmseYmDjpwuAmjGZC8VZKCkyhhSnW0UEkBA6XiqVWNskPUmOUszTTBLMtOjRy2M8HRXHzCIrCao3nZSaGE6jPTcHN0NNNKVJhFa9jfKBRapQf+RROF3BEgiToAFdcQRUO5bM8QTvUbB0VL4j+0ucOMelA/n88J0XYO9RsW5LDo0UpaukuPl4kpSzp1b6OCxs5azEWayo7xAdVUFHOXBQvSe9DjHYUCmUKygFlMgd3/K+ytbXFu+++u+9YHwTBz5X7x/vXaDR6KI3Xz8P6U1XM9mDG98OKTz/99Ceicj6UJVbwCC7+36Kn/1eU9ng0znusy+h3OiilmW+1MPmFLWSQPB3XkzuEvx9HzKnKNpVv0IDTQoUE5PSaz89UhrIpoFDeo3wmp+ZBhs8UjUqZwEzxNvfJcwj8k+2AKYnJaTpApVtklLFhgyAbCCU6qInLPAZXPISedvBBjAvLwpgzJUhnhLMd+r6C2XoDH7ZoFAwq6+GLB9HDm/jqcXTnbXz1KKpzDV9aQg3u4aMaJpviCstoj9DxswkU5tDtt/HlVVT3HXz9JCoZYFtPYNpvYeN5QjtgOtaEy89SHN3BR4fFBLhyCN94lGDzFezCk1BaRWViQaQma9jqMcxkr2sT/8dw42UGxdOUfY/F6XVmC09B/y7xzuvsxCcpz7YJVRtfO0qYTXGVA3mxOY4zMcH975CtPI+a9bHNcwT3XyZdfhqtIjxjqsM1PLUc1htiOtex9eMoUyRbvEiw8TJ28Qn06D528SJqcAeCMrr7HhSaUuAn27jWOfTOmxAUyebOoWd9evERGs0mwb1v4Ron8VEFPW1LuGfdoAe3wTp8oYrZelWIE/XjEIFKx/h4jqxyFGUnmJ3XUekUVz2MLy8RpVuEoxEqKuOiBpSKeDw6HYveKyhA/SQ+LKJ0jM0S0tkIN+ujxrcwRmG0wRiNDoKcCBXh4wLWKSY+ISjX2Y98UXv3gJe/ZmO0H+SdVZSTnqRAejI57NmJzORMGa8j8YacbmF0BUuMKy6g3DSfPXvpoNI2rngAXziU329WvCsjB+GcQJsuy4vYQYgX5N5KdsTuK5qTBACfCgsSLQ4h5n0uIKaMyqSgqf2UgJA96YHaP8MG6PJZDix9kQNIcdlLiN7c3GQ2m/HKK6/sx7G8PyH6s1ifJmX6F53Zz3jtFaNPCit+2OMfWHgdnsX5/wI9/X+itGeSTBn1hpRKRarlKtqpvMPSKGcFcrEZ3hthOOXzhD33bOUsaIV3kukk4YU5vx/2CyHeyWnbZUBCoFKmg20iYyg1F1E6xHmHysZiB6UjEa/aEirtolUq3ZcqEbib6CzElxYgGaBn9/DxogzJ0wEuqqFsih7fx8WLQmt2GWM1TyFZQ1UOUAkNymdCi5+18fUzYjlVFcEvhQWwOUvTWQquA2ldjIwLywI5BTWo5BE7QVkKYHERPbhHWj/NeOcuMzPHglvDpzG+elTo1eWD6M1XyVqP5Wa7G/ln6YkeyiuCze9jF59BqQLB2rfJVj6HMiXqm28ymX+SsFinsPEK2cozqEKN5Z23GC8+ixtuYHbeZDc+RoEOQdyk0LmBrx8lm3uM4O4fkR14CZVNyBYvEK59l2z5OXxgGIfztHbfxjbP4MM6rlUl2HodO3cGZQ3Z6kuYrddwzZOYnSvYuUchHclMyWaYzVfJli7K76B2ApQivPU10uVnhXTkPdnBL6MGdwh2rmDnn0D370JYEqG1naFnHVz5IIRlgvvfARNh587hw6rAkcpgW0/igxA9baMGd4iTLq5wEBVW0MP7oiELijLjLC3Jn8qLq0zWJVSKMDYQt/DMkVjF1DqS1GITTxiGhGFIFIZ4PEkiieOyvefXBDYniczET9OOJIMsKMqMOajgw0qeaJ6i0l2ZAyqNKy7h4iVUVMfPJnmB1CJTmdzHlY/gioeE9YgCl6CTbckyK6xIAbWpzIoLkoMmQvaOQN3hHFiL8kO8qZL5SNxEzDyYKtguBI2cWJLJtWsHEFZFVhMUxFxBSxyNFHFFNve/+sD+Mzc3x9zcHJVKhbW1NQ4cOEC73ebKlStYa/cTopvN5qcWLj9sMfvTmjINPwfF7EFmZjs7O1y9evUTwYo/7fHwkIPR6Ams+8/w/m8wGg6ot5oUTSzQR65Hw+anzj13Fu2l60K+pozCu5ym7GVgLVCkAWxeuACc6GH2OjsVMZ46ZllMMY6olETHQjYAVcyhRHEaUGkP5axYEgFqtoPCkeo6mS4RTLcBjYtX0UkPdCgwymRTrJ0Ky+jRfXxQZpBq7LRDFsxTLRRyNmANPevKZjDZxYdVcdDIDYGxU7GHSgcMwkMU7RRfPZFHvBxDd97C1c9A0sUXl2TArww2bTO7/zq6fJBgOsQtPYPuvoMnQKUDfNzCLT6L2bmMrR3Hxw0hf8YtzNZrZPNPQuucFLHlZ8kWL2C238TOnWFYOUW5fwM/dxq7+CRm+w1s6yzZ0tOUNr5HuvoCqlRncfctRs0nsNM+/axAtHkdW1okaD1F6c43yA5+XqJVVl8kuPdNksVncD4kaz1GuP2aFCodkS0/h9l8Fdd8BD24J1Bl7zauvIrZ+KEQOYqr6OkutnWW8NbXsEsX8SZGOUt66Jcw25eoTsfQWkKPNnCFBbKK2G6RJfh4nmDjFTETrh9BZeLIYecfx5sipnMFNe3jaocEip3uonMfRVt/hJ7tUAsUKhlJRlntJERlyKbowd1cdyYXso9quOICRBXZpL0lZkqBEYoh3k5xmcWPnIiBFRI4uRliTIAKQjyhSDtCme2qqJWzGHPzgGyATrswuS/Xc1THh3MCmbvZPsToVYhONygnA3waQ2EVb/PUaOch6YouM17Ex9IiKTcDO8QVllChwGcqHUhwbdiQ+zXtQzwP1MAN0d7jg6YwSMMi6EaeV1bN71cnDj9WkhnI//Rk+aFVY0vP4oOln7qdOOcIw/AnEqLb7Ta7u7vcuHGDIAj2u7Zms/mJD+3vf42HLWZ/GlOm4eegmAE/Son9kJWmKf1+nzRNPzGs+ONr7xf7MCeW8XjMpUspyv4PeerUdyhGgbiCeC9xI/uD7j1htcm/pqRj2/u+PXdxlVOavUbSZ20eRZHJTYnKv6YYDYfMZimBCQmjgswcHOATlJ2ifYL3Dq/r+EAgELI+GoXLoZWQTUwGFOfl/6V9MY91Ql/2piqFarqDjRfp9XoYN6NQX2XWuQuZ3k+D9pXDqN4NfFyDWVdMeUur8rX6CXTvBq52nFJ6H9s8SZgOcY2z6FlHCBbd6/jaUXReVNLBFt20RqNSIgwVo9EQ1b2Or5+SGVz5IHr7kjjYzz2OGm1C3ED1b+GrR7BzjxOuf59s4Sns8nOYzju4+nFs6zR6tAU+Ji0eoDDexReauOYZ9OAevrxCtvw5wvVXyJaews4/SWX9+2QHX4Jshp3FmEmbSVphWDjH/O1vMpq/QGQG+INfIrr7DVR8HOUs2crnMOs/wDVPCTlk+VmCnSu42hHM1uvYhSdQsy6uegjdvYnXIa71CCoZkK2+iGlfBZdiF55AJ32yxqP0urvMb1/GV4+gxzugNa56RLwWp7uifVOa8PbX8eUlbOuMdH12iqs/gpsvo6c78tx2hmucApcR7LxJOQFtWvjqssxl7QSVzQDwpRVc7ViejEwevDmSnDrvc2hN6PY+rEPURJkCSgcorZnOEibTKdoYbJYRoIhCTUggVlyui5omgMJFJdFkmYq4kJgS5O4fHp0fkGao0T2UUrjSQZJoldT1iJXGOy+WWNMerrSKL6zIfMs7SSdXCT5qyG3oPKQjeU6Tb9bpBB8XUEFNOivlgQIwFRZyUMzdS5S48dihuIq4ROZ9OpCDpxL7JZGOiily1vxffOh+8uPzrPcnRB8+fBhrLb1ej06nw927d3nrrbeoVCo0m839hOiP28M+TWf2C5jxZ7R6vR6XLl0C4MCBAw9vdfIAwuv3r62tLd544w2Wl5fZ3X2KaXCGkvpnoDORrigpwsrnbVmepqv8nlGx3u/evNd4pRGWiM41aDb3f8yLmBIfOOs0/V4P7T3NRp3hoI92Y1SaADHehPigITdbJjY/3megK7mma4hOdvCmSKqqxHjUdAMfVHFRAz1rg5sK+SMR7dHMzDPeXSMOoNA6AIPbzBSgY0lYLh9BDdclEsZrlBviK0eFxl4/hRrcxpcPoDvvkKkI03kXygsSGlqYR80G+MZJSCfY5mmyrbcY6nkW/Bqq+hgkQ8ZmiYqaSkErzsOsh126iN59W07MpiBszcZJgo1XyBpnyFaex7Sv4iqHcI0TqGkfoireFNBJhvehnBucaI183IRZHxVVyJYuYnau4BonyQ68SHD762SHPo8pNFBKE9kpzkSMK89T2nqFTukkpt/H15+m3rmEq1Yxk64UsO3XpYB13sPOnUMP13D14wT3vkW2/Ix0wmUh+AR3/0i6vXSEbZwSfdO9b2OXLkgn5R12+XPo4ZoQPhrHMJuv4UvzUtTywpUtP4uyU4K7fySd18ITcsjJdqXrmn9CCBbTbdnggxoTGxIAZv1lue6CGF9exRfn5Nq1U9SsJ2zXHDLzgRAyMEFOt1e5o9uezZwc1HRgQHvqjTrOObJkRpomTEczlEsJA0+kLSYwaJsKFB8WxfnDFCT1YbyOtimu0MIXFvDhqRxClNdTLhX2bDSHj1qg43zWbCHpgwpzq7WJHC7TCRRKeRYZYq1mioj9lBPzAZ3H22S55Z0uinmwjsnzj2R2Zqeif3PjfJY2Bl3Cu0S0qMpjK78kzvkfsj6Omm+M2e/KTpw4QZIkdDod2u02V69eJUkSGo0GzWZzH7b8cZTq0xBAftGZfcbLe8+dO3d45513OH78OGmafqo8sU8ivH7/cs7x7rvvcufOHc6dO8fq6irf+c53mNkncbUaevSPQO8xEoXo4XM7K7Xn4eicaGt8hlb5mTZv2PIPmWPsIOJrMTSeZTO6vRHFQp1KuSzTNp9hifJCmclJ2isZPgcVnDN5yvAwd0aIIFwEOyLyfZQv4XOigpq1xZhYF2TeFpQZzSDp3KJQqhIXaujRXdJ4ETfalZiV6kmBGEtL+caR4IqrqKQnYZDTvgim7QxfPYJP2rhiDWViFGNxfJju4LMp3ln6E48PV2hUSijdQG2/hWucoJLcxM4/jsnnPWq6iRrv4ptnYNLG6wgzuIMrzJOuPE+wdRlnl7GNR9DTtpAJvBMdblgj6lwjCw9D3EL1buJqx1CmiEpGeOtQboZtPYrp38YV50mP/DLhna9jVy7mRa+DtjNKLsMd/gJz6z8gaZzCjXfZLp2jtf0Oo+IBisM2aeMs8eguvrSIWX8Vu3xRBNrzjxPcfwXXOIortCR0My+cdv68CG2DkPTQlzHtq5hsCjTQnRu42gEoLqKn27jSCpiQ4O43cLXDuNqRfC4Wkq2+ICLs3auoZJjDnhbdfkcYj4WmzBddgk7WUbqAaz4iaeE41LSN3n1Lug7v8myzJQgLIlp2UymI6UC6f3KN5F5QWT7HivEYC7pbRpsIY0IKYYwrVrEEJNYzyjLS2ZQwSSmqPiEJhgxfWhQnkspJtJvKfMpnco27VGQPlJnpqhBA7Cx3tc9EN1hcQkXNfdmLclM85bzY5aiIVyiMRBiqPRutorwOgdwTjERTpyvgRqAK8jpOoVRB7tm9x6hofw7vjcGrElnzo4MsHxQCjKKIpaUllpaW8N4zmUxot9u0221u376N1nq/a2u1WhQKhYfqzPbgzl/MzD7F+nGYMU1T3nzzTbrd7j6seP36dSaTyad6nU9azKbTKa+//jpJkvD888/vt91aa3l89DzOe/Twd+VC9h6vlTjug7AaHTlNX6Oc3h+l7RtxC6Cfw4oGr0I8muFgyHg8olapUijE8v3Oi4OCN+Lk7pAb2CbS1dkeiiCfA8xBlqCyHooxPqiS6Rqxm6CSrswkTBk9XkeZCBstMO5u4pIBpcYBIjfK06cPo2d9vFKSFzbZkY4vEScSHy+KuLqUQ2dxHSY7koMV1AndEKdbBHaGqxwWnVnjDK57i+4sopbdxzSPC3uyuIBvnUJlCYmuU17/IX7pcZgN8LXjou/avYarHEDZFNs8g9m+jJoOsfOPo0cbMBv+yGasMI9uX8VVjzEpHaLWfRsfnsc3TmI2XsPNncOVltDd9/C1w6I3K6+gpl1MlpEd/grB3W9h588I6WHWFYJM5wZ25RnC7SvY2iFq27dQB56jsnuNadAg3LjMdvEY5d4uunyc8q3/SHYon7XNn0ePtzG9y9jlp1DJlOzQl9DdG6hxG7twTtz5m6ewyYTi1jV8/RRm5xo+KGKbJ3NCxphs6RnUdJfg1h/i6odx9aOoSQeCGDt3Hq8DzPg+DLaF2BHW0b07EvUTlsFVsFETpT06HcnpKihhm6cFWgPpYu1E5nF7YZraQNzEFVrCQswFz3uEB4BZkjCdjKlXJaRS2QTvU3Q2RNuEyE5Fc1lqkFFh5iqM0xlkE4KJxdghQVwmNAY120HbMa4wh4vnUEEFP26jXSYHwWwg90VQQznRZHpUbgRQlMOekxvRKyWZavlpUnlBSuTUA3sWc96L9IY9Qbgp5Z1bDH6G3zMTVpEwjlUs1HwVgvfYxq9I8f2I9Wl0ZkopSqUSpVKJgwcP4pyj3+/TbrdZX1/n2rVr+3q2YrFIlmX73rafZP1x2ll91uvnopi9f+3BiuVymRdffJEoEqfqzyJter8YfcTa3d3l9ddfZ25ujqeffvoDF8IHEp/jF3A49PC/khM+TpiLitwtXPQ1ylkwGpXJ15wCs0dXthpQeBXgHPQ6baxztBo1Qq0E0sjF14Gfon2KykCKn8ltgUpyak2nKDdAZfJ1H83hswyVjYlslyyYIwxrqFkH7ab4wiI2tYx2hDFWah0hnG3igwquMC8GsyrAOoMe3sMXFlHjbXApvriCGt7Blw+iRuvC6vKgsrHMz/o3makGlf67+OajQsevnyRt36STlqkVwFSfQQ/XxP1j5w2Z6aRDMiJs6wxmuIWPqujt17ELj6OSoUgakgF6vCvzpd4ddPc2rrwoRVSXxdS3tISdO4+5/wphuMS4+STV7dex9ePY5WcI1r6LbZ7GNU9htt7ANU+CinBhFe1SdPc26cGXCDZ+gKus4osLkA5QKsBsX8EunEd3bjI1Dcqbl7DLFygP13CLj7K08UMG80+TjTtsFx+hdfMbTJqnMXGJsLgI5RWCW18nO/QF1HgXVzsK1SOY7ctCGmnfwMct2sWjLNpUqPOFBuHdb+CqR6RwpcKkyw5/CTXeIrj/fXzUwLaOo4f3wUR5h3NIglgzca+w5QNgDNHWNQrrt1Ba4+MGrnZYGHl2ih5vS3HSkhDtTQxhAafzPDJyQGBf9G/fJyfxKJugcx2lUlqgSRWLFZzJUF46P2VCQqUIgiLoOt5OsaMN1Pgu6VAxDObQhToFUyOyGSpLhBVsJwQWUHMSeZSNBaJUWjolXZBuyru84Ci5P1wmaIXSYDPZ+VQAWS5FwIj9FsJCzl0PhKGrY/l8ugBkKF3A+1S6MnKNqNb4cBFb/+9/7D70WdpZaa1pNBo0Gg1AZEudTocbN27Q7Xb55je/Sa1W2+/aqtXqRxbS8Xj8i87s0673w4onTpzg2LFjP+Gt+GnTpj/KOd97z3vvvcd7773H6dOnOXTo0E/g0D9RDOOXcBj04B/ljFzptGR47fOiRq4dFbd9jxFhJ3k3qhRpmtHtDohMQKNRRu9vEJBTIfFe5R2ZGBer3BMPb+SmDSp4L5i+sjNhbJkSPqiT6YSCHaEyhP7sy9hxm8Foho4b1KPZvtYGm6FnPVxQQSVdiq6NK5xFj9clfiZeQmc9iWmZDWWjVwEqm+BqJwSKbJ4l3LxJVjtFNNnFlw+SbL3DmBILahMVH0b1buKrh8WncfECanAXX1yitvMK3j0GUQ2Cgsyg7r+KW3gc5abY4ipmfB+z8ZrMh9KhuK4kfdAFgQy3XsfP+tjV54jWXsW5GenqCwRbr+OTEdmBl4SwkY6E4bj+Q1z9KMQV/LQHcQ3TvUm2/DTB1lv4dIqrHsQzQZWWMPdeJl25iBlfx7ZOEdz5FtmhF1GzDnblIrU73yI78iXK2ZSk9DRh7z38CLrBPGEUopY+T2XzMtQOoIZb+LhCtvIcundHTvXphMZ4A994EqIqKhmKJdasT3DrP+LmTuNKCyKCDitkB16CWQ/dvY1yGa5xDD24J3BzXJeCXAjEesymJKZJMHcaExfF83C0KXMymwoVvrwkXbgnJ1jcR8+6AkEC+7TdnOAkBAnJPgu9AqvQ0wxvAgm9DAqShxbmXZ9PBa6cbAqBSYe48gpB9TDUDhFkYyKbMHPS6WXJLkrv4oqLeNUkUD3JCdMBey46Xhdy5mshd7PXUpx0JLpJbVCzUZ7TV8jlMx5MtG8mjlKQ5bDmHolLu9xjVclraYVXLkdYNPickq8gnf9ffqJ9yDm3f0j/rFcQBCwsLLC5uUmtVmNhYWF/3nb37l289x+AJPe6OIAkSUiS5GdazP7ZP/tn/NZv/RadTodnnnmGf/gP/yFHjhz5TJ7756KYpWnK5cuX6fV6XLx48acq0D9t2jR8eGeWJAlvvPEGw+GQZ599lnq9/lMf/4HObG/Fzwv+3v/dnOVEflMgw23yovaBsD8nPuJKM5nM6PcnVMoVysWiuDHkmTL7nnZO4U2GRTKg0KCsBBwKqWGEYpbffGVcWJBcqWwMWRfjUzLTIFYBarrLNPX0J4ZqsUZJj3KLq3nR1gAuqKGH93DKMNILVGZtKVpoSaCO5wV21HkgYdLGl1bQ/bv48gpqcA+nYtRsgI2rDPp9vGlRrdbRNPFWCrTq3xZroGkPX1mBdEqvcJKFwRq+fgzVfhdXP4GbPy9SgKCI2X0LN3cOFVTQXQmvxE1xpQMC2U06IlTu3MBsX6FXOUV5toXZfgu78Bi6fxu9/RZ2+SJ69ypq5xp25SJm6zIua+LLy/JaxXnM7rtk82cx3Zsyv2ocBwyueZLwzreZFU9TdSnZ8gWC975GdvQr4op/+AsEd76FXX6SSCv8gujL5rauMC4/hhttsRUdpzDqUsp6uKohGl7DtU7gsxlquMkwWmVh7WV8oYFdOCs0+rBMevhLmP5tgnvfxbUewasA3b+HDyu4ubPC/pt2gABbO4JyKcHa9+X3WprD1Y+S6SI6G6P9VIpXaQnCEl6ZXLA8Q2VT5BSGWFft2VcFIfup0Xs5ZIr9efFsOiGZTYji0j4TkqSPsVOUT/A6xhXnRNtYbwhc7mbSWdtECCbeEaRdTFDA1xbwag432SXNxoxtiHMe22+j4gZF5dGzHkSSZeYx6Gwq7iFhFXSASnp4VcaHJSlA6RTCGsoYVJbrLHWAtzM8Cu1T6dqUF3hS/OzwWPns3uaaMo/SABpbOIsvPvaJ9qE/LjsrrTXFYpFiscjq6ireewaDAe12+wOuJM1mk6tXr3L27FmAnxmb8b333uO3fuu3+Of//J8zPz/P3/27f5e//Jf/8qdyyn//+rkoZleuXME5xwsvvPChJ5bPAmb8ac/R6/V47bXXqNVqvPDCCx+Zcvqh7yF+HlfTUtCyJC8q4PMZGloweG3kVEYQ4Jxn0B+QzkY0G3NEYZyzGuW0602Y4/o5pV/t6dTyf2vR74iezUshdVNhNoLM4MI63luUH0gkTFCimxRx0yGtSkRgFC5cQSc9iYUJxLtPj+7hi4t4a4ncFi4+jEmHQt4oLAhFP6qDTcQouHJM2IeVQ6juTXxcI8w6cvMMBxT9iLB5DD3dwpVX0H6CKx+QOZopoPr3UMNt8AlRmmAXTmDsBN98ZH/G5U2MN0V89RDm/vexyxegtCwdrLXo9rvYudOYwRpm7RXsytOoyS7l9g3SxklCk6HbN3D1I6igj958E7f4KHqwjln/IXbpKXTnOqp9Hdc6JQWtvEKw/TZ2/rRYXO1cw7VOgonJFh5j4f4ruOYX0XZKdvBFghtfwx75vDjxH3wBs3MVH5ah0BCh88GXKN//PnbxccqjTWblFSbpAuHgDru6TuP2d0mrh+RgMNsgmzsr46z3/iNu7hSusoSe9nHFJWz9OLp/D737Lr66Ct5hti7vd2KuuIjOBoDGzp3FxTVU0sdsXaE5GxFMAlzjGL5Ql852+B45HVGQgLAkm38Qk+/YeRfk8nma3c8QA5uTej0mzTCZhSyULiguyOHOe6G7e4EflU1ypqTMOdVkF6UcLmziiy1cWEGnPdSsD3EdE5UIzARnY6wLKNgu09mYnnUoNUZHmpLvojEQNnK0oJ8ToSpS1Gbb+HgBgoq4eEQVkbOkQwl91RE+G0shs1O5Nr3dL7BiXWX3Pg4oJyiMiUjn/9NPvA/9cRgN/zQCiFKKWq1GrVbj6NGj+64k29vb/O2//be5ceMG9Xqd3/7t3+bP/Jk/80CmFJ9kvf766zz77LM89dRTAPzar/0av/Zrv/aZPf/PRTjn+fPnuXDhwke23p8FzPj+YuS95/bt27z88sscOXKEp5566mPjuj9y5hY/h6v9r2Uovn+xi8OHRLBLtpL3nsxCu7NN6iytxhxRlAuoUblWZS8gFPY2D+NTCey0Iznt2qEwF63EZkgAYD2Pr4/FzDXtodIhmamR+iL9bpsw3aXZaGCKc+A9erKVe+DVYLIN2UisftIpylsSVUaPNvHZFMKmpCwXFuXQbhN87ZQwGmvHZZ5WXoaghiWia5sUI0O4dA493sSXD2B2rwljbPeqnJxnA1zzFIRFfPkAcdZDDTdR6QSSMW75Imq6C0FJHqMi7NKTAslhYNLBF+bwxTnCu9/BlZfyWdib+LBOUlolHG9LMSwvo0Y74hNYP4xu38QVF3H1o5h7L4sdVFDBbFzGF+YhneFqhzBbb+OLC7jyKnrnmszutKFdPkN4+5v5bDQlO/olzP0fQpaipgPs3KP4sIxu3xQfzFmP9OBLqOEGBCXi4V2qakJ04Ama1RJZ9SjMxsT3v0+mYkaTlCSxJAc/L3T+298RiDmbYoYb+GILu/qsbLqTDq6wIFZiay8TrL+Kmo0l5scU0MkQhcbOPcpu5RyzpacFYhtto0ZbYFN81MAVlnCFPGF6sI7ZeA1z/2XM+iuYzVcxm5cwO1cw7XfQvVvowRpqvCswbzYR2jwiOVE+kZkxGq9DcRbRMcwG0iH33kWNNvA6xtZO4EqHBLmc5eJ/InHAcZnMhgEz20V5TVBdpFJr0Gy1qIcJgVGMXZF2b0S/vcG4v8vM53EzaQ+ck5w0n+BtKocMZ+VGDcoitlZGDogg79NJorz3lh9VMMSGa9+my2ArXxJ/x0+4HlYD9iDrk8zl9lxJzpw5w6uvvsq/+lf/CoD79+/zq7/6q7RaLf7m3/ybn9l7OnPmDN/4xje4dOkSvV6P3/3d3+UrX/nKZ/b8PxedWRiGH9t1fRYw414xexhvx73Hf6Q8IL6Ar//n0Pt/ofxYrn2n9t0UlPIkqWU86lKMS1TLFWGJWSdDdQVKKzEyRgk8mQ+vNQ63J1j1eSCgU+ATwfxdHiSqInEhD2N8rkEzaY8k9YSlOuWyxJ8w3YGgLA4gsz64Pj6eQ2WJuPOHZXCOUnYPFx4S9HS6ja8chnQsdlpRE5308HELNe3lpAHNtL/NTJWoBSlRU8IyXeMketYX/dV4F18/itq5iq8fwWxexs0/CtMu/cIx5k2GLzTRu29Lh1haRDmLmztLcP9V3MKj+PKKDOcLTaHBLz6JXXwMs34Ju3heTH3HO+ADrCkQZFkODwVCAPAeX5xHjbbxxSZu4Rxm/VWy5SfRQYHg3vfIDn5OBLn1w5jtt7Fzp3H14+j2LXx1FeUc6cHnCdYv4RbOoLIB2eqz6PZ1CGIp9sU5bKElMObcaczuu7jWSdmwMyH4mLVXsEtPEoUziGPSxiHm730fV6jTLx1BjdYgKKAXnqU8XieY7uLmzqBH2zBYx5cWsc2T6GQI2RTXPIWPa+jROsGdbwLgmifxpXlUNqKY7GCmGYQxvrIqBzC8wIt2lpMnAtGdFeYgCPNDmmHfb3FvqfeZAeDJxkNcOpFObNIR8sleUYgquOI8rrQs8LCfyUwu7YOv5NClkDy8lY7Ke4seb+OKC/igjjN7v0OLSjaFcFReohQUUWGCVTGZr5CkKdPeFkMVYsKYMJsQ6wm6OIcyCpIexPUfWcYFFVQ2wqswv19V7vto8mIaiGej0vmwIP/MUZNs7ld5kPUn1Zl93CqVSkRRxO/93u8B8NZbb31qBvn716OPPsqf+3N/jhdffBGAo0eP8vWvf/0ze/6fi87sk9hSfVYw43g85rvf/S5JkvDCCy88kAj7E72H+El8/b/AByWZfe0NyrUiczAa96lW69SqdZRy0rEpmTfIQFnLbeQlnVexN28zOB+I36Iu4nV1n2bvdSnX0qh83jGSSAznGCYBozTGBBG1INunZ/uwCelIbK2CIj5soie74C0+bkEyQE13meiWFC+X4CuHxEVBaZyKxEnDlFH9OzJLs5bZ9ruMbUw9vY+Kaqidt2UO0bspkOe4jY8qYD2+eQK8wtUOoTq3UB7q45vYuIFKJ7jFpyCbQjKFwTpq0idduYga7eLREqKpAuzCYwT3X8F7jZs/hx5u5QP6ID9Ra/RoS0gNaPRwU6jb1soBO52C91IsN9/Eh2WyhfMEN78hTikeES1vvy208tZJ9Gib0E5QyQi7chHduyeM0vEOrnUKH1ZQo10Y76DSCXblGdRgHV9awqz9QGZH1YNSQ+bPEtz8hnSNUR1tE9rVM6jWMeZ6V6gXI4qhJpzs0nVVNuOTTPo72FGfLGqh+vcJ7r0sP9tCS147m+KjBunqC6QHXxTPjp2r6N1385lSQdDw9g3pvravoHu3hSSCkbDLsIaPqtKJZIkU4PEWerCG7t1Ed97F7LyVP+81dO82erqLzmZ4U8CWD2IbZ7Ctc9j6KRHOe4dOh0LO8LkN3GwgBBPv8VFLcufG26iZpDv4qJ7fQwaTDgnSnrjqhy25tpI+Ph3jgwY6LBPrlHLBUGsdoN5cpKjHpJmlO4Lezj36wwFTG+FmXcDkUGcm17KdgAmFjm9CYS3qPb9VDUqTT8JBadK5vyjF9QHWH1cxe9DXeD8tXynFuXPnuHjx4mf2nl5++WX+7b/9t3zjG99gc3OTr371q/z5P//nP9L96UHWz0Ux+yTr/UbBD7um0yn37t1jeXmZZ5555oHx4E9C7QcgPodv/DUIS6AU1jt2O208nnK5TqlYwuPel1tmcqrzHvVZ7WvVhDQiOjS3p0fTuVP43skxp+n7sCpQoy7gvGHY28aOtilHoMKy0LVViEp66LSLj+dwQQVmXQnvLC6BjoSCrwsQLxC7gaQph3XUeEsIG1mKHq3tkz0IK2S6yrizyaR4hFbBMYnzmVhpSeaIKhJoctaGdCbkj3Sax5IU8JUVfFhhFjYx3bsyj9u5JkQQZfCN46jeHXR/A1deRlmLqx0h2LgE6ZRs9VlMbw2ck4LvwYclCsN7WFPIhcyXZIMuLWI2LuPiGj4so0Y78nP0TkyB2zcBTXbgeYIbfyiuI2hs8wRm5x3IEmz9KCpL0NMBaryDnTuDdxY1HaJ7a/i4jm09gh615fvaN6X7TCe4+jHM1lvozm1caQllU7IDz4CzBLe+KTlndobSEemRL4KzFHo3KZQbzOkR83qILy7SLx5i2O8yTKBfOkaaOYJbX8esXxJ0OiyjZx30VDZ/u3geu/ock3AOnU3QM/FmdJWD2MYJyUAzBdRoC7P5hhS5zUuYrTcxO9fQ3ZvowTpq3BYShVdC6Q8r+EJDDgtBQa5nl0pitE/lGs+9SNWsjxquo8YbkKViMVY+LESW0QYqGeJUUQTrSueEC48eroFNScNWriFz6MkOKpvhonmULkA2lqDYoCzC+LSPUYqwskq9UqDVqlKpLxHgmE4mtHsZ/d37jEZTkiQBHI44n3lHIr5HSFheOZTe68lkD3LFU7jqiw+0h8BnS83/sPUwndme+8enMTj+qPUv/sW/4Fd+5Ve4ePEilUqF3/zN3+TWrVtcvnz5M3n+nwuY8ZOsIJB508NcCNZa3n77bbrdLvPz85w6deqh3sPHwozvX/FpfPP/QLL5t+m0bxMZcRbXRktXIQFnePZEnflpTwsl2OcedcoricLQGr9vf+Xy4mdz/doe9Cj2Q9ZCt5+idZFGc57pqJP762V408CHJVQylKBJlGRL2akUHzQ+bqHHW6ADZqZBxWaodEfytkYb8nLVo6jxDr68TDJLGPXbhNVDNILk/8fefwdbkuX3feDnnJPm+nvfvc+78rarva2e6cEMHAekSEgBBFYrEYogpV0uCRFcUdhYAhC1QRHBFRlSiFwK1AZJieYPgNygaGJJQOACg/E9pqfLdXWXr3pVz7vrXWaec/aPk/d19bSrel3VbChwIjrqVXVl5n31MvN3ft/f14A3geytYYM8eDkwESasIeM2duwkoreFrZ5E7N50s6vtdzDVk4j2KrEqYHIZZJBFJDFi6wq2NAudLfTUs4jmXVcEhw0IyiSzLzutWGEOXXKiahsUULu30GNHGOQXKGxdwMy/iJ44g7f0TZL5VzDjp/HTrynMIDffQU894ajthRlkex2bq5Ec+iLezd9HH3wNgUCPn3QztPICg3CcnAI1aGPjGFOacV1sew3ZWnUzrYnTyPodbH4Cdfc76LkXXNdZnAfAu/01kgOfc1ZTuXHi0iL+8nfJWh/sJKqzjslPosuLyJYL4RSlBQr1qyAzJGOHia1A9xr0YmhmT+B5PoXdJfy4BX4WUz0GWOTuLZA+QTLE+DMQFh1kqJ3PJ+Bmr5lxFziqwvRFrpyxwXvgRUapJ+kyYBNM0nLBm50t504iJdZzzEKbq2IKiwg0Iu46UlLcxWbKbn46kpsoBSJE9FZdZxhWscoDPKxO8KJdyBUx+WlH7IjbbpMbppTyuOdE3V4BEA7GDIoIIVGiS65QJGctBkuUGHTUot3xoF13WXlEaG1RKkaIjIPrhXSd2cjCRwYkU7+wr/fIZzWc83H7Mmqt2d7e3vt9u92m2+1+Imen+9dnopg9KMwID/9D6vV6nDt3DinlnmJ+v+uBOzMcwWR5U3Hz+o/z7IH/jbIfs1vfxjjXU8dSBKc9G0XI2JENVpx2Xe4BGjlx2zReZY9FZux9g2kNRhNHAzrtLrkwIJetYJWHkQV0Gk0hdQcbJ871W2acCLm/ifXzmGAMMag7skY4hhUBgb6DtWUIa4jOqrM/UjkXsJmp0m/sEA9aZMuzZONtbDCJ6Kzj6y5WB4jWXWeWm1LbZfMupjiH7Dcw1WPIYRsz8SSitYwtzFFafhNTeBLRWccU5xG+M0S2UZ945wc0MvNkox4yM06+fgOR7aAnnkJ2N9zcsF+H3AS6etxR0gtH6Iw/Q2n1ByQTZ0gOvIZ373WSySdJFj6Hd/vrJPMvYiafwFt+g2T2ORdJEpSdx6PWJEd+3BWd+RcRVqAnzqA2LxNQwFYOYII8orWGbNzDFmcw5UPIxhKIFrK3ix47jOxuoSfP4N36OnrmKWxYdKzHA5/Du/NNTGXRsRWHHaLpF+jX18hsvOX+jVprID1nbZUzzqsxO4PNVvDWL+DbBF07ji3PY3t1Ym3ohlMMvVmUiMk3N/CJkEJAaYKo36TQXkdtveXuN+W7opGrOgg63VChh4goch2WGbqZo7XvhstajStixrEfwwJCSxIvjylX03y/UfBmClOKXurFGDrY2aQuNr5z1ZfddWTUdh19btalRguBjLpg61hRQgcT+Egn7JfS3ZNGOwE0xjEwpQ9RHcIK+CVIuo7oofLYpIdQWaQwhGGAyIyTR5PYMr1uk0h71Ou7CCkIwoQgkPiZDFKkjiFIdOWPYB+C9HH/etyd2X43/Z1O57H6Mr7yyiv82T/7Z/nbf/tvMzk5yT/8h/+QyclJzpw580jO/5koZg+y9mMUvLGxwaVLl5ibm+PEiRPcuXOHVqu178/woHM7rTVvv/02W1tbPP3MT1Au/Ths/xrIuhNcKuFc9wVpUVOpUatxO2B53w5QCGeVJR2rSjByXpBuSE/KHLHQ7XbodWNKxTEyfloUkwjP9LFGglfDWOWCMuMOQgwcy8+bcmy3wbYTsOamHHzGgEgW3Gypv+2G9snQmeP6JfpbtzA6IVdZIOivYYtziO4uSEmkKuSHTczYIac/K84jd29g81PI7euQrTq3i0wVop2U0BHRzh2m0t3CFiZRa+cwU0+RtLepR3mKOcmEaRJ7BUx3i63gAIXOKmJ4HZGr4WuNKC2i1s9jSgskC6+SW/ouUX6GZOFzqI23MIVpkoVXUetvYUqzJIe/hHfvO+jacZL5l/GWvk0y+ywiKGJN4rrD9jrJoS/h3f0WevIJhNAkk08SLl9AdjYgP4mpHHBzs+YyZKuY6hGn/wrL+Pe+R7L4MmLQIpl9HlW/DSZBT51xtlaLn0N0NvHuvUGy8BKqvYbFI1k466DTqI8tL6JWfoDNVDC1o66bSgaYmvNXlPWbrmMMi4iJk4TxAJI+CYqhqNExEhNHZNptPJugVRZRPeHo6cLpB8WwhWytpgSQFM5PhdFWujkavu/EylLt3Z/vEVAP+igTIaKmi0cRnvN2TENphXVwng0rEFScIXZvG1Td5Zbl59IuUWKNdrZr2UlsZsIRQ3oxKulAEjrXftIiZuM9WJ+kC4GXOty7mZeVGZeMrXyEl3ceop7vhOLKxwqLJyWep7BKUixkiQ1E0ZDuoE/c6+D7IUHg4xdmMdWf2/eM5nHPzEYb9v3CjI9r/ezP/izXr1/n13/911lfX+f06dP85m/+5seyyB90/YEpZiOj4Aeh5xtjuHbtGsvLy5w5c4bp6WngIWHCD1gPcryLizmPlJJXX32VTCYNo5z8b4h3/gKe2Bl9Q04jNtKrGBy8kmj38Gsn3Bz1rO86flgHBZEyy1KZWbPeQGvN2MQEnvRTFrGBRGNInAYtaiGFh5EBBDVX7KIGgi7GLwEuNkQkMSYog9bkkg2ghslNIqImAkFMjmj9HYxXID82jYqa2NIhiNrYTMllavXWifKL5JIetuxc3m1p0X3+4oxjjenEfWfDuvu2ojZeItClGhKBnngCvXGDlihQi9cQs09jh1186SFtTLa/zHDyFKa7w3AwJOmvOvFv6SSF5jXEsEu7+iTZzj1EcxU9fgrZ2UC0t9ATp9yLO0lI5s+iNi5hoyHxwS/gL30LPX4CsjVsdwehAuTObeLFz+OtvIEZO4RIWjRzC0wOG2DWIVNJC9oKYtBG9HYxY4cR/V301NN4136X5KDzadRjhxBG4938Ksmh1xC9BmRrJIdmURuX0TKDp2PUzk1MeQHyk4j+Dqa4gA1yeDe/is1V0JNPuqIW97CFWeLacQff1ZdcQkFxBi9Xxu9uUIy6GC9DpPK0TJ56rJBxREZu4/s+nu8jghImrDhYUHqpCzy4+ey7s+q9P0vNs11ChHaz0STCS9rIZAfrhe7nERQxQRGCUhoououo38Jma5hMCZGbcbljIiVYDOuI4S66MI8pLOBucg39HYTJosMxfBm4bjEZQlgC6zl5gVRI4WOsM+R282YvNTRQqe7Suvw4q91ntDHIEGsTDD7SJgipCJQiCD0QObQVxEnCMEm4tPU52hvfeo+TxsP4GT5umHG04X7YazzulGkhBL/yK7/Cr/zKrzyW838mitmDDhwfhJ4/GAw4f/48SZJw9uzZ9+w0Pikj8uOO39ra4uLFi8zMzHDy5Mn33kyqxBZ/nmn5v2Bt0w2TE8VeiKfUDk6TMp1FpEnV0tuztkoZw6kRqkQISRRFNOt1fAWVShFpk5R6LvZEqdbLkiQK6xWde33cc9IBL4sNx7E6cmnROnJsMiuQwyZWR/S8MUKciwJejmGnRdS+iy3MUfSloysX56FfT10RFKK7SaLy5DvLUJ5xlk1CgjSIuIvJuPmZyc84qKh6EtHdxJYOEC6fh7iEaK/SkSUiWaZUKCHVGGL1Anr8JLK36xiQXpZw9zp27BCZuI+unEZsXUE3brEVLpLvbeKZJXr5aYrKOpp9WHL5clEXk6s6A+H2Bnr8NLJxF7V9k3jxc3grP8AUpqE4he1tQbaCt/EOyczzjtWYGycbNdFTR1CtZUS/6bRlpTlkdweCIt6975EsvOzsqA68hnf3e5ixA5Atg/CIj/4E3vIb2KxLZZZRh2TqKUx3B3/njhONr13EhiVMbWQ0PHRkEcC7+x2wBj37LFYIx+L0QkztGFZ6yGHLQaVGYArz2CBL0G8w1rqK7zn5h1Yh/aBKhwDpB/ieIpA9fDt017PpTBaT6rJG9795txuTHiZTwoYlEj+P9St4xSLCxu5ei3uo/o7rAoMiJqyBl3OHI0FKxGAnhZYXMLk5FzYLzpMx2nVp2tkJbKfvNnqJTi3PhPtcJK4QCs/FsaBBZEBEbo7qBW7zJpwtlQCsFKC120SOrOf2uky1pxeVQiClIpPx8Cuf59np/5hOp8Pu7i5bW1t7Thq1Wm0vTPPDzH2tdZE5jxNm3G8x+4OcZQafkWL2oOvjisn29jYXLlxgcnKS06dPv++G+aTF7MNmZtZabty4wZ07d/biYj74+Azb9s8ynv832M5FpLSOTi8Nwjg83qZaMiuV07+gQFiEkK5A4XavIOn3+rSbdfK5gHyaBj1y/8bi9DJW4CU9EmOAXOrhaEC7Xa3QHfBy2KAC8cBR9YXnLH6SiFCvg3AD/HjnDoMoxh87Stb0QCqMV0S015wuLY4Qw11McZFs8wo6N0nQb4BN3MytvYwtH0Tu3MDWjiM3L2NrxxE7N52f4LBBJ3+Ykh6yqyYotG+RmziB6q1ji7OYydOIfgvrF1ArPyCZfhqpsm53riO83RuYyScI2itMdteIxo8waO4iBk1aA4H0AlQgCE0PmSkDqdODn0f0G5jSLLLfxNt8Bz33PGrjbWwywIwddKbAxVm8tQskM884diIKVb+DqR5CdDYRgLf+Dsn0KeSgQzLzNN6N3yU5/CVHz194CdFaRq1fRs887eZpcy8gejvI+h3M5Cm89ctExVnauYOEydCRHII83s2vYkrTmPETKX0eV9SkQm5fRQ0amMpBbFBwIm3hYcOUJCGkI6YkEdYLaWUXKE3MIZSH0BG5qEV+2MLELfQgwRjNwIL0fERQRGVyyOBdMghA6qmddjrumRBW40cdsBrpua7Hehl3L4uUAg+gnDmC6K4hOquYwhwmN4MI+6lbjoVhHXTPaQFJdV3JEKn7DqKUpO4vCfieY8vuMSed/ykSLMrVpiR2Th6Y1LbLOAMuYRAoR/JQHsZahExNC7CphE66wFB/jGTqP0UIQbFYpFgscuDAAbTWe/6HN2/epN/v75n71mo1isXi3oZ9v4XmYdaIV/CwrMTHPTN73Ot/F8XMWsvNmze5ffs2p06dYn5+/qGOf5jr/zDMGEURFy9epNfr8corr3ykSefe9Sf/byD/Dqb5XYTQ6TzMgpKgbQoljuZi7lGWWMyoNTPQbrfo9XpUygUynqM9WytcNpZNQSFjnZOC8MG4HTIM0t1wButnQMbpjr+evgBrzsmhvw0qJFZlTJzQb9+mZ3NUKhP4YogNi5BEyM6qYzn2dp1Wp3QI2d0kyk7jYd1u3C8ghi1M7ZQTTI+fckzIscOI1io2O4bcfgebnybXuUcrnCArengLLyJ729ixg8iV824+hAvoNOMn8dYuoSdPI+MOJjcBVqDufhe98ALCLxJ0d0hUAEoS5iuY1hpxP6KhCmS37iL8PKI4Saa3A2EREQ8dmcPLuIIzeQpZX0Ktv4OeOuWIF9UjeEvfIZl/EXo3MJkqavUSyfSTrputHMC//R2SA6+41OlDP4p382vo+edh0MIWZtHFedTyG+jZZ5A7t7HlWZLZ51D1JUx+AtVep9zvYseecXOmZEAy9yIi7jmIMT+BnjyZxr4EmOoxtJ9BdrcRrXUnTyiOQ9JDLX0HvAAb5LHleUxQQMuhm5EKXKFTIRSmEV4GT3pYIdA6IYqGRNGQpB+jhhF+EDgyhO+lwZ3gXG2023jp2N0TNnZaR5tgpbOMwss5clHrHkiJKcygiwvIpJ9ymGy6mWqgiwuQn3GO+Ma49AgpXPwRPZcZqI3rrPZS24VzxlcZJwMwEVbkEFK50FolHewoU1cRz8faxFlYod3fS98lktHMGqxKY4WQxNP/mUMfPuC5Hh8fZ3x8HHDo0Chv7N69ewDvca2Hx1vM9ksw6Xa7TExMPIZP9Omsz0Qxe9AdxAfNzKIo4sKFC/T7fV5++WVKpdJHHv8oYcaRr2O5XObs2bMPZIcVx84NgYlfAFHDNv4NYBEjyIOUAm0Vrr0yqUZn4OKZEDSbDbS21Kpj+Nj0pZLqYaxId62u47PCxyrQwqa5T3HakaU5ViKAoOx2uFEDYZpY4WGzU4i4i6936CUSVIVaRiOlda4hvU2n8Ulp7G42UkZEbWxuArG74SJGVNaJgfOTaeGqOQuqoAhGY/OTgMQWFxlGEbHMkDc9shkfdm5hSzOIQRcz9zyicQ+TnUBtXCYZPw5TT7hOzcuj1i+iJ5/ATOZc8Rk/6lzwhxoZ91HtdUT1EH7jLrloi+HkCcTubczWDbaysxS6G6ggRORreFhM+YA7z8QJRGcLde8cev5ZxLCDmT6Df+ebDAsnKSIwtaP4S99xJI94QLLwEt613yM59qOIqEty+IuozcuObKM1+Dnig59HbV4FP4torKCUh6keToXCGdq5MhO3voEtTLpCOuyAF5Ic/AIMmqiVH4Dw0VOnkO0NR4EPi46Gb6K0e3OfzWYqYIbI+hL+sEU1jlCDjGM/ZstuPqZjxGAztZKK8YDQpvCitRijMV2DMQYtAOUjvQAZ5BBh3m1uwgpDHbq6E3rIYcMRYqzG5J3Vlg0KqQVbytI1CaK/mbqNVJ1zitHu3h92XaqzX3SF0VrXjQnpLKZwxUxEfUzgrLJEEmGVQojQsShFNoUejYPs9RCh/NTU2HfmwdamDvypvdUoLX4kjlZgy69iC8880Hsik8kwOzu7Z+57f97YlStXALh58ya1Wo1KpfLIIcf9zuQe98zsca/PRDF70PXDM7N6vc758+epVCoPVEweJcx47949rly58oFxNQ9yPADj/yF4JezOP3VdlCM2OpsmnHRMjLKVpIcFtnfrhEpRHqshhYEkTnenTr8mrU31aMY9+NYiTeQeWqwzXg0y7u8kA0h6aYCiwAZjrrsb7CKjLkObpW9CCqJHIeNDZgKrE0RnDYIC1iu6Tis34eYQgwYmLCM7myg9wMgisnEHWzmE3L7mClp7zX0Oi0uQLkwjult0ZIWkWycJq2RCic1V3N8ddmHQRPSa2OI0xAP0zFOuKxs7kuaY+ejxEym1/llHvBh2QXr4vU2G+TkQA9S9N0gWXkC2N8isfB+9+AqyvUG2cZvu5FPoxgpy8xb13Ayh6OLlpslsXsOMH8WoAO/Od0kWXkQkfeK5F5i6/S3iyo+g9IBk/gW8G18lOfwjbq51/CddR7b4IrK9hR4/5diCO3cw44dQu0uY8eOpiHgTG1Twlr6DnjxNUpjCq285mYCO8a5/BTN2EDO2iOg3wAvQ869A0nOEk6iHqR6CQQu1fQMbFrHFGWxhzAnUE6chs6UFEpVhp9WmVi2h4r6bqVmd6hYtyBATVlxcixc4mv5oroVACYvWmjgaEsdDdNTHS4b4wwhfaDLDPiZThKCGztQQYdmlVAuV6ig9JwfprjlT5Nwkwss4xxKjsTp2Pon5ScdO1ImDHo1FKJXOx0Tq0hEDButl3XOiI/BzjvGL+17QPQcjp1ox8N33k1LsR2xH92ykxt4jKUza9OHXiGf+s329M4QQlMtlyuUyhw4dotls8uabb2Kt5erVqwyHQyqVyl7nVigUPrFoeb/ej3+QU6bhM1TMfjht+oPW/S4gd+7c4caNGxw7dowDBw58KpZYSimstVy6dImtrS2ee+45arXaQx3/PjZk5Y+6Dm3776bO9ymmblJTU5wubZjEWKPJ58oUsiF74Z4jmAWV4vvasQSNTudnIEhQxvngud2ncsavKg331DFEHeSggVUBNijT7fUZtrbJCY2Xn8Rm8s4KS7t4e9nbceSS3BSi38DqISY7jmwsYcMiWgmCYQM7fhTR3cCW5t1n8vOYsOSK4NhRqC/RoEKmsURm6iR6/TI2cwrRWsWUFlza9dhhxO5t6NUdUSUqoKefRna2sJmKYwDWjpPMvYjcXcKWZx2dPT9JEo6R37qIPvAyUoX4179OfOhVmMzi3fwG8cFXkV6Gwt3XSY58AdGrk9m9Tbd6grjXpG9z5FbeJi4vEE6cJLz9bZKDZxHxgM3Kk0zd+ArJ0R91adJHv4R3/fdJDr+G6DeIj3wJb+0CNj+BbCxjSzPouadRG1cw1YOo5TcxkyfTmdwuycRp1NYNQj2kXTjqXtAqcDO3zgbene9iyvPY4gSycddpA2vHXDHq18FYNzfzssjGbdTqjvs5V+YxBaeJkoMW2aiB6uM6kKCM9UMX7yIEVlhEKubfC+C0iYO/0/e8h0AFPpnQx9oCSRyRxAN6wx7gY2ON7XZROYXnZwCL7K45KUFhynVgQRmSroP8rIGo5QpdUE7nZWkMC9qxevUQ6+UwMnCJ0XEMYQGkcN6fmTGEn0szzVLPRQyoLCR9Z2Sthwg/g9VD1wFak5KkUlhx73lLvzJgfY947v/ygfDifpaUEqUUJ06cwFpLv9/fgyTv3LmDUoqxsbE9Msl+cs8+STH7g5oyDZ+hYvYgSylFFEV7rssfln32Ucd/kmLmLG/coPQ9tPsHXFLKD6b2l18GVcGu/w8I2wVpMIAwLval1WozGPawQlEo5NOOy+y5gmBHP8YRAUSn03kv1QhZtPFw1kCO4i+SPtjUVFZlnbu61YioR7+xQpRYCuOzdBtNZNRy8GJYRgy7yN6mg4xEiOxtYUWA9UtOV1WYhiRB2gHD3BxB1MZmq5AkCGMwYcWFfxZmsJ0d6pQJdB9/7inUsE0nv0ChuYytzqJWUwPfxjK2esTlnmWrqM2rmHiAzVZAx+iZZ1Ar5zDVw5jiNCJJIFdFrV7ElA/TGztJ6fa3SeZfJDnwMt7yOfTMGZLFl9Kvn3R/fvPrJAdfxU6coLh6keTAKzDsEg9DgtYq7WCMdvEYYze/xWD2WbxkSHTkxwlupAVs0CE5/hN4t7/lPlNjGT39FKK97mC89gbCy5DMPIVqrWIqi8jNa6AC9MxpxKCDGTtALALG734HEc+ix48henUISiSHv4BoryO3bmCzVWygUCvnsZkSpjgLuXGIuggTYwvTJNWjWKWQ3R3UxhVH+jEJUhaxIgDPQ8QDZHvD2YrtWXrYd/Vje+y+1J1GKKwfIFToOjfl4wd5/GwN5BSt5i4q6aO6m9jWXfoygylM4mVmCXMGaROscZChGLZdqGt+CpGpue5MhSmT1zqixrCNzWWdhRWgkgGICiLIO7lHkE/JSn2sn3VxL1EHERbTc4BQGawxCOm75yXNY7MmxnVpo+/V/Sqk2xgbKdFjP4nNnXyo5/yj1v3zLCEEuVyOXC63Z+jQbDb3Zm1vv/02hUJhr2urVCoPBB/+YWf2B2AZY7h79y6VSuUjs88+bI06q/2IFre2trhw4QIAzzzzzEMXMvgYB5HCCVj4NezKfwuDNYRQJDqh0djFGhgbm2B3e9PBg1LuzdcQ3t47xzGoRzMFzxFKkC45Xgydj55JtW1GO+hF9x1d3/YwRrHbiYACY2UPpXsMTZ8kO0HgOco9wnPi6UEToRuYcAzR20WaDqYwj4y7WAGJKhH0N6E0Cf0GIupj89PI3VvYsUPY9cs0bZGC6RKWJ6GzjQ2yCJ2QFGdQwnd09F4d/Bxy5bybX3V30FNnkO01rLEOigxK6Pnnkc0VUKGD7UrT6NmnKNx6nc7YcZIDZ1HrV9C1Q+iZp5CNFWxxEjPzlHPBL8+RHPwc3t03SGafIpl7Hu/6V0kOv0YgFShFtd8izlTozTxHdu0CveJh+tsr9OdepbT0ffT8c8jWOsnBz6PWLmGK08jNq9jaEUy2gty9h/VyeMvnSGafRkZdTHEGvBDv2lfQ8y84b8R4yE7tKaoZgXf7dczEUYyQrrvLVtBzzzlH+n4Tk5vAZsuo9ctOWpGrYmoHnT/ioO1ezF4WPXkSvAzaJAy21sjrgbNCswa8jIMlgyyojJsfjWzXxKhbEemr3jiBv47TRPMeorPpDKGxeGQR2Qp+dQp0hIr7RIlm0O/Ti3rkTAsVBFCcw8/PIIYNZDxwcy5rXFqEUIio4/weg5yrp8M2Jp8lljlCk2C0RXhpF6GH4GccXK588POIuOvy2PTAFTkTufmZdT6hdgRXjkyChUwbtJFdFZA7gJn6jx76Of+o9VHzLCklY2NjjI2NceTIEaIo2mNJvv322yRJ8j5t2wchUvshgFhr6fV6f8hmfBTro2BGay3Ly8t7UeDPP//8vnDl+y2xHrSY3U+7P336NJcuXXro695//Y+OkBmHhV+Dlf+WQeNt6o06UTaHUAAA+w9JREFUGRUwVimn/nAqpS6DG67ZPcsgK13UjHPcGTmBy73dqbUjB4aRWaoE6bsdurXE/S7d5hahH5DPZRwcKD2gg4pbzv4qO+lmPP26o1yrDLKz7lKOM+OpvZCHRRH2logy42R7u+5zFmYRnTVM5TDJ9hIdnSMfCEK/7PbEUQfrZwn7G27n39/BFichyLsiXD2E6DWc7fLaRfSkS18248ed84WOsIUpZ147dgh57w107Qid6efJ7F5HhAF64jiyt+uE3dkxiCPwBLY0jRi0IbQkCy+g1t/GVA+QHPmRFDb8HKTu+f6wiRcUMYdepXj7+5iJo9j2BhuV01TuXSKqHCDTeQc9eRq/swF+CblxFVOex9SOINpr6Nox/OtfRc89iw3LCD0kPvga3volRNQnmX0WP25AYZL4yI8gmyuozRuY8SPQ2XGFuDCBHTvonFySIaa8gMmWkVEXde/N1KMyhxk/ivVDRL+FiNdBKPy4D7LgLKg835EdbLob0knqHJM4rZZxIuORel8I6YhGynPkokwVB8lFDo7spdo06zZantX48Q45L4euThGbGkmvTtTcIpEhWRnhBQaVr+FZ6wTgfjadbzltoC1ksOEYQidI3QVZQSgfhi4lQHg5l+YQ5F0AKL5jUNrEwYwmSUXR2j03aedl5ShF+l3SlREAEusVief/i30/6x+2HmYjHQQBU1NTTE1NYa2l2+2yu7vLzs4ON2/exPf9vcJWrVb3OAP7JYB0Op0/7Mwe59Jac/nyZba3t5mZmUEIse8B6f3F7EEsVD6Idv/222/vG6r8UJjxvmW9kHviT9Hc+essViLKYR6h3SzDCjcJkBYnujbpy0WMWFgCjMCOxKw49pe0CdJGjt1lccN0x0NGWEkv0rQ7fQrFSXJhgIj7jhatNVplSFSeUEfIaMPNWFQWupvIURhnHCGjJsYvIAZN5LBNlJvG721DqYoNio4FWD5Af2eNgc1SLBfwlcB4OWTUwdaOIvp1esUjFKMdbHURuXEFM34MseVe5MKCUVkQylHac2PInTvOYqq9CVEf0W9i4wF68WXU2kU8WaRfOkjRRM4hIk02xs8iWuuuAMoQTMfFkdihK3qNFcjGDja88TX0wrMQlty//7CDjIfslI4y0dmC8gzZ3i7DxRcJtm7QlzmC22+wO3aEUBpCP4/X3kS21tFTJxGDpiuamzfAJuj5Z5FRFz1xEoQguPcm2iuBHnNwZLaKLs85mDLqY4vTiN4uauMqJj+OqR3C+hoZD5xGcPopTJhDJCmE2FpFJEMnvs5ViKV1AaKt28hBPYUUYU88NvpVOiIEyoVr4gVYL0R4AVgflIcVGScP8AKEjpDxLuFgC9nfwJRc0KfIjCHiDkoPkH4O8gVycZ84LBNHQ3Rnk3Y/xvM8PD8iMIIgabhuMTPm7tdhHZubQssCMulg/QoidOe1fh6RpqRbP4swQ4QISXd96aORhmwqP+UoWrfpkyKl+AMYjJQI5ZHM/mnwHzwe6kHXfmnzQggKhQKFQoHFxUW01nuQ5J07d7h8+fKetm0wGOyrmP3hzOwxrk6nw/nz5/F9n1dffZW1tTUajca+zyeEeGCz4Gazyfnz5ykWi+9hSj6M2fAPr4879n5Px2ee/TXK+muw/i+w0oCR6L3tMY51CGBdlIwYxVUo5bLC9ubYqQbIjqiS7L28rE3oddpEwyHVfBFfxY5U4ucxCITt4+sWKjbYgitKctiBuOeG7BYYtkH6GL+EbK+66IzSIv7uKklQxno5xKCFDkv0V6+TqAyVbAY13E1hxzvOBmp3CVuZJ2zcJS7O4MV9zPQZRGcLWzuKWn8HM3ECtX0dXTuKTOEwEQ1Qy+fQ0084inZlEbXxDrbfdPOq7SXUsI3NObjKZsdQWzdcp1Sedx6NtSOYwiRy5xa2soCwFlOYQA46iMYqydEv4t1+HT1xFMKSEwH3WhS6q+j5M6jWCjYzRmbzbfTsk/jdHWz2EGM7N+iWD9LQWcIoRoQFite/Snz4c6hkiBk/jEXgXf0K+oBjSaJ8+vMvE2/fJbd5HTN+DNlcddBxeRZdmET2m+BlSGaeRMQDvFvfAsCMu+9DxB1Up+e65Nykg+oEju037OCZGGwWm6ti8zUHx3k+o/BNm87J3q1xI4afBZNgTYyIu4jubhrzorFegMlPEYVVCKfJeiB05OBH5WJciDrua78IOnJdbm4cEUhClUEPu+j+Du2kBFaidIusbSJLc6iwmjqSJE5iYo1Dcry86wpF4L4Pk6RwepxeN3EO+iMTbynugzNT3odNv0fhTAsG5S+QK724r2f849ajsrJSSu11ZEePHmU4HO4RSba2tlyifZLsCbez2exHnm8EM/5hZ/YI1g93W2tra7z11lssLCxw/PhxpJSPNG36o9by8jLvvPPOB9LuP4m/40cd2+/3OXfuHEKI+8gl/wHIeezq/wRqmMKFqTsINsX3pdOUkYo8USB16s6Q7kClwiBcFHxKPTba0Gj3wAaUazU8IdyLx8Yw7LthuZch8SuuIA4aCKEcbdsYZw7rBQ5m6jeQvVVH0TcaEbVJwrKDtnoRUaZGvPw2ZKuUMiFy0MKW5xGNey4CZveW6zY2b2IICJtLUKwhem1stuJYcFNPQL+BqRzAW73kild7A12eR/p5ZNNFzsjGXfT0GWTjLnLzOklmHOKhK8S7S5CroidPopbPOaPhmWfwlr6HqR7CjB9Drb6FqR5EeBmMl7jsgp07JIfOou69iSlMQWEck/PQ3QHe+tuYmScQ3TqmOIu6/T304nMQD6F2iGJzjUKmRFSbR/ea1KtPULnyFTpjRxFhgSAIsMd/HG/tMkQ9zOwZguYyAy+Hnj2CbK5BkmAqc6i1y0ihMBNHMIUpROTkB8n881g/RLbWUCsXHOw4toDNjzsrqd07WM93L3UVoGUGmxtzhA6TppnHEZihE9lj3DzVjJiM0buztSB0Ya5eDhuWXROnY7CxA6/1EGF8B3FHHaeby084mFAqZK+OyUpH1NCRg82HbrYmc+P4YUgofeisMggCBnGRuLGLb/vIbIUEz0XL+BVH97eR81k0ccq2FE5Qrfz0mZDps2DcfGxvlyffNekemXlb6Il5wtr/gcfVnzwuk+EwDJmZmWFmZoYrV65gjCGXy7G5ucn169fJZDJ7xe+D7LaiKCJJkk+lmP3lv/yXeeedd/hn/+yfPdLzfmaK2WgZY7hy5Qqrq6s89dRTTE1N7f2/R5U2/WHnGOWebW5ufijt/pN2Zh9UzHZ2djh//jzT09OcOnXqvTd77UUIpuH2X8eINYybdqUiNJxpqjRgUg2OFJCMXEScg4iQEotKB/qCeDik2WziK49yucwojdn66Q5aJYhogEjaeHHXacqyY44oMmyBibG5ccdQ7LvUZ1OYRfYboHxMUCFo3kIb6MsJkrXryNIs+cB3Lg3VIzBoYKtHEIM2trII2mDLM5h2H6M8N+votUH1obcNmbFUW2RcseruYrJVvHs/QM8+jZtzOPKEuvtGKnDuorptTDxAdoUrVmuXsb0meuEF1MolxLBLcuAVvJUL2GEHPfs0avk8tjyLzVawvTrkqsjNmyRzz6E23nHFsTxD5BcwoUTdfRM9/4zrDMeP4N35Pnr2SQiKmIqEZEhm5TzxwZfIRD300S+S3byG3F6jXjmKat2G7CxBUZLduIrNTxH2d5GbfUw1NRoeNDDFaWyuglp/x80La4cxpRkndNYxZCro8rxTUPWbyO42JJFzTMmPO4it3yLbXUHdvct7WHwivV+U7yJUlO+KnZQgAwcpKt9R1IVwMzkh0z8PEHGM6O0S9loIU8KOzWGLc8io6+J+sA6e9h3T1gofOdh0ji5hBWzkYO/elktfKEySkT450cOUxomTGD1oIKxkt2vIDLaQ2QJBEOKJtHhZjZAeduQbaay7p0nzyPZILMpJEKTakxsIBDYzzp32H+P0Y/RN/DSCOY0xZLNZDh48yMGDB0mShEaj8aF2W4VCgU6nA/DYCSCXL1/m7/29v8e3v/3tR37uz1Qx6/f7nD9/Hmstr7766vvw28dZzEZu9+/tjD74+E/Smd1/7fv1ch9lw0VxAU78dbob/wlaSDycPkamLyEh0qwzKRGaVJ+T+jmmGjSbWmP1ez06zTr5TIZ8xolK9xjYVgC+i/sICwhtMSrBS4aIwQ54RWxYQQy7bjAvQ8dm7NeRgzomU0EkMbK1QuIXiQd9RH2VcOIIoU1AgAnHkJ1tTHYM0d5ww/6oD8kQG5Txkh2Swjih1ekcbRc7fgKxcwtbmEJtXUdXFp0VFx5m+owjR9QOIXfvOp9EL4daewc9fhiAJFOFqIFcewc9cwa5cwd17zzJ3NOo+l285Qsk80+htm6iVi65Gdba28hhFzO2iOxsu0iajauYiePI3bvInSWEzWOyZYT0UUtvYOaexgqFnjyBXL+KLYxjihMI4ZPMP4v/zu+RHP+ig2onj4G1jN99k2jqFKazzVBl2cgukh228OMhUWWW8N55CPPoyePuZR0PnAQhU0Q2V/BufwcrBGb2CUAgd5bS2VbG5Z8p37lspEbSKI8oUyVbqbhcMS9lBKcv+tGcaUSKEOnXjJzr9dDNRQcNt6mRykkDChOIykH67JBT2kUBZctYFTgvRqPB98GCbK+ji7OYfLpRNQmiu+3CTbOTCCucODw/6VxldIzvSYLCGL3dOuXKGImOiYd9Wv2eI7UECj+TIwgSpJ9eT44yAkcVKyV6yHTWnD4jVoDxsiSH/kuSrVuPLWkZ/t0Ec3qe9x67rR/Wtv25P/fnOHbsGDMzM9Tr9Y90Ufoky1rLL/7iL/ILv/ALHD58+JGf//H+qz7E2tzc5Nvf/jalUomXX375AweRnuc9UATMR60PKmZbW1u8/vrrVCoVXn755Y+k3X+Sgnp/Z5YkCRcuXGBpaYkXX3zxwwvZaIV5VuT/mUgdc4NsITHS9WkO/xdpBJUrapDOA0Ywi7G02i06rSblcoF8Lpvqikasx/QAk9Kthy1HaxY+ico5SyE9QAzq7trZmttJdzZBhc4Jf9iGYQudm0J3W5gkIjd1lIwZ4piXnhNVZ8rI+hLpPwSivQWZMnL3NrFfILNzE7wsYvMKNixBewtbO5J2ZU8hO9sgfdT2NWwcoWuHHYuxOIVa+j7GyzmoMHaEl0xjCV094LRnt76LqSxgyvN49y5gSnOYyjze3QuY6kFXtO58Dz19EixuVleYQEQ9bGkWtX4VU1nEBkWy/U3ksI8NC5jx48jlS4io5/49Jo6CNaiVt7HKxd0kp34Sb+kNxLAHvSYkMfGRz+P164RWU8hlmYo2kZkKncI8/VaDpizT9MZQV7+GunsBqzJYL0QOu5CtEh96Fb3wPKK9jdy6CcOeswqzoFbfQt19w3Vy7W1AYPw8sZfH+nkwGtndRbU3UM01ZHMF2VhG7i4ht2/irb+DWr2EWj6HXLuMaK5AHGNyVZKJE+jJJ7BjhyEsvTtLtaQsWONIJyrA+gVkbxf6u871IzvuIL8kQvQ2Has2N54Wsbq7V8KSgzb1MKXKe46ViEFJj0wmS7FSpTo2RrGYR3kew16Hnd0G9d1dur0eUZJgrXHlOS3We4VKglUSIwVGeej5/xOEc59K1ti/65TpbDbL3NwcTz75JK+99hq//uu/zuLiIq1WiyNHjnDmzBn+4l/8i7z++uuP9HP9g3/wD7h48SIHDhzgt3/7t5213yNcn5nOzFrLqVOnPtRxHh59Z3a/QfFHud0/qs8wKmbdbpdz587h+z5nz54lDMMHPD4gPvhfwO6/xO78G4TKuZmGlCl1f0QKIe3SrIMAASTEg4ixagU/hZasCN3/UAL3l6zToRntXMZNjJf0HDyZCbFBxfnqDdpIHWFkBnK5VPzq2IzGDulv3iFWOZTn4w1c9AfRANnZwZYXEK01bK4GwkPEfez4MWdtNXmSYPMuw/Ii+fa2s7raugW5MVh9Bzs2j2htOIbjoIWeOoNavYSuHnKu94Uaev4ZvM1rjsY+7KKDMjpryNz4FsmhVxBBDrX6Fnr6FGbiiOvmyjPu681bmNoBhJ/Bu/V99IHnEe1N1O030IdeQHR2MZV51OplkumTDLt9Mq1NRK7i8sWmTqLqd13HU5jA5iaw2Rre9W+THPs8olsnOXQW0VhF7tzDTB5F7dzF1A45g97GMrY8T37jOoEFtfgMJuqRDLo0qieJjKV64zsoq4lnz6CyeVRzDetnMOU5bOAYjGLYcpl02bE0Pdp3sHFri6C7QyWJUJ1gj6KOCpwFlhc4iNFXe7DcyHDXsRvdrFZEA6yXMgOFRBjj5qPJ0DFv/RpWFZC9TWQ8wBTGHWs0jVkRg5aj4Ocn0lTr1AotPwGZsrt/k6HrKlXWbbCscvebbSJMhPBC1315AYGICbI5l0cmJNFwQJRo+q0u1sQE2YAgzOKHPioI0tmzHI3O0DM/hy0/Dzz+YvNpwIwPI5r2PI8f/dEfpVAo8Du/8zvcu3ePr3zlK/zbf/tv+c53vsPZs2cfyWfqdDr8lb/yVzhy5Airq6v85m/+Jn/jb/wNfvu3f3tfmt0PWp+ZYjY9Pf2xXdejKGajmdfDuN1/0PH7WaMb7PXXX99Lv36YB2cP4jzyp8CfxG78AxAZ91CqdEaQ+s65shaTJNCoNxACKrUqntFpZ5d61I3iqnCNmk2dHqwfABatjMuUirsI3Qd85z6hU1KINZhMFWHAtNbo9IeI/CQ53UcP2lBeRLTXAYkdO+isrwqTYAxCDzG5GrK7g82OITq7JH4eL46w+TFAOGsqoRAlYDhwL8ztW+nf30HPPo3sbmNK06jlC+iJY+iJo4ioD9kxssuXaFeOkSw8i7p3Hj37hGMItjaxuTFHMBn23Iu5OIFo72BzZczME6h7F9AzZzCTId61b5Ic/bzLRKsdxFu+RJKZxhSqqG7ddWTFSUz1IPTqyI3r6MkjCOmRnPwS3o3X0QtPuyJWnkEXJ1FrV5xP48pbmPIsZuK4s7XKj9M1HrWrX8WWJlGzp8kMO1hriQrP0NUWv74EG23iTAVTniHsreLpCBvksPkaJjcOGPe54iEAtjBOkqvR7EWMTUxyP5jmCBKkPKJ3u/t3IcYEEfed7VmvjlXSWUTla9hMGZspI4ZtgvYaqmuhNIHJTThGo5CgU3ixNAOFScc2NM6GyxSnXXCn23GlM7us21ipkd0UYDVGKifqTiLwQ7fp8gOsdhEvUkAmkyUjJVYKEh0xjCL6wz6tbgfpSYIwQ5jLoMIAMfVT2PE/kv4bOFLVpxHP8jjXfgrmiJZfqVT4mZ/5GX7mZ37mkX6mf/Wv/hW9Xo/f+q3folqt8ku/9Eu89NJL/MZv/AZ/+k//6Udyjc9MMXuQNXLNt9buG9f2PI9ut8vrr7/+Ptr9g36G/czMRvMxgBMnTrCwsPDQ53gPgWTxj0FmCnv7/4kl62IrhAVpQTvS1iDSNHd3yefydDpdJ36VAhJxXz6ac4EQNhXIJjatajIN1FRoL4MNU8f9YRcRDx00lKmCThDDLlG/S2PoU8zlyfqGgfWIvQKiuY7NlMDLugiUsAiDTrozH0du38SW5hA7dyDIoQZ9PN2HTA7RWsdU5pHdHUxhGkGHKJjFHzZd+GRnCzHsYgvjiGEfvfA8auMaujwHww5W1RiMn6S4dgmyz2Jmn0S2tjCFMcSI2YZ0qdClGef5ZwwiduazZuoEavM6evwQyeLzeFe+QnL8i4ioh548RuXuRWzpaUxpGtFvILfuYKoL2Nw4OlvBWzqHXngG0WsSH/sCavUyhAXnBJKrkCw8g2quYrI1xKCD3F7CzD+JySlUu+k6yWSAd+3rzvlj9gkyvTqhF2BnjpOoAN3agfY2w6hHlKmibIbszhJer+7yu/wMpjwDmTJGKWw0xIsbqPoye7sYRqbUxsk4TOwgvdQyDSkxuSomV0EUptGluXR+10XEA6chzJaxXpbYL+ApH1J3DdHZdNE4xVkozTnShU5cBFBxFjIVh3brAfgZN18bUeVH9HrhQxxhvQCRWIT0EaSZZUqlUoK06Jkk1cW5dtL3fbwwIC8kRkAUDxlGCbv9Ntv90/TVCarJXWq12h5C8rg7s4d53+xn7Wcu1+12yefzj21euLq6ygsvvEC16rR7nudx5syZvXfio1ifmWL2IP+IIzrpJ2nVh8Mhm5ubHD16lMOHDz/0D28/nVmSJFy8eJF224Uq7jcz6H1syMkXIPgf4epfwNgEIXLprlrQqrfodXuMjVUIwxy9Tidl5SuENOnXwhG90kLmICX77ovNgtJdRAIkylH7sxU354p6iMEuVmZox5J4qKmG4GV8NyPpLBMMB5ipw24GF3WcwXAzdc3PjSPqKw527O5iM2Xws8hOl6gwR9DbxY4fRm5cd7+uvMVuZoagfYtWYY4sHWTpIJn+thMAt7eg10ZPHnfC6eIU6u55RGmR9sQZyo01bHkG64dObxYWkVu30JPHoDCBWr2Mnn8KgUTsLmPGDyKMxlTmkLsr2PI0yZHP4739uyQnv4TQMc3yQcaXL6Fnn8Dmqmg/h1q/jpk84nRgRz6Hd/u76IWnUNu3MdMnEb06ot1zbvj3LqJnn3CzvV4DPXsa7+Z3CYIcnfJBx1BUPsnR12DYQd27AICdPY3sbBMYjR8WsTPHMYDs1tHDPl0TkuQWHdtPCcKoi9e6ijQWqRNyOkIkWeeEksmDCl1ul1CpBdqeSDF1AEnNr5MY4kEKRwbufpCOxi+SGJvJkKgMMu4h60uY0iymNJu69gsnatd955+Zqbj7IB46CzLhY0hT1nXi7K0A4r4rcn4Goq77nEkfG+ZAR04cPSp6Jt2sifRFPso7G5FZlCCjsvhZQW7yLNmJn2dnZ4fd3V1u3bq1V2R2dnYYHx9/LEXnswYzjtbjTpmem5tjMBi858/u3r3LF77whUd2jc8MAeRB1v0OHg+7tNa89dZbtFotpqenOXLkyL4tsR7m+p1Oh9dffx2tNWfPnkUIsW825AdS+ysz8PQ/BlnBJhtoBDs7u/QHfbfbzOYcoyulLu/pa5woDRg5owvXbakQq3Kp1VEWS9a9ZIx2RWnQdPZZYRHjV2g1G9juLpVSEVWeBSucN6KXZ+hXHCnECoxfQNbvYcMCNltFDFrY6kFHEsiWISyBTojyU8i45+C6YRc7eQzd77ATTpGJWmQmDlLrroAMEGvvsBX5dLp9uoV5iHqI3VXQGjHooQ+8SNhaQfWbmLE552cZFlGbt8BKzMRRvFvfw1rHBvSufwsrFLZ2ALV80bleSN9BkZ1dxLBPcuon8K583c1cDMTzz+Atv4UY9p334fxTyPXrLjOu1yA58jnE9l3n7n/vUup0fxiiIbp2CO/qNxC9Bro0iUhi9PzTxNVD1FbPI+trTm7Q2UUg0AdeQM8+hWhtIDp1twEwBnX7u/grbxHGPTKVSfLThymWSmTMkKTfpTXU7HrjtMqH6U2eplE+TjL3DKZ2CJOrYYK8g/ZSKzKEdIQL6WZoVqX6xKjvPku37iQVCGymgslWEf0Wcue2i7/JTTrDaem5AtPbdSbRmYqDE01axCwI4TpkKxQynakh0gQIo8HLgB66a3lZN7PzMmk0TJBqLeHdAjwqxik3U6RUXenkJ4mwmImXsAf+DLlcjoWFBZ5++mlee+01jh49CsDS0hLf/OY3+cEPfsCdO3dotVofm+jxoOvfBZvxQVan03ms7h9f/vKXuXr1Kn//7/99VlZW+Dt/5+9w8eJFfuInfuKRXeMz05k9yBrdBEmSPJTJ8P20+5mZmfcJBh9mPQzMuLGxscfeOXbs2J4DySMtZgCZDLz0v9D9/i/R3fk3IA8wMTmJEhISnbrrW4wdQZF+GjUzio8RWOW5mUWqTcO4GYr1fLSxEJSxJnHi2riPSXq0Ox2sV6A8VnRU7UHDOfDnxhH1dbxEY8JxRK/hPBFL887VXcfYwhSiu4MVXqpX28KW5shsXyMuTCG3bmJzVZLtFTpRQjbMkKnOYKzFTh0jl0QwvsBEfZVBYQaxu8RWOEkYdVFSkOvcQ4QNepOnkY11iBNEr47N19DTp/BufZdk5hTJkVfxbnybZO4J9NHP413/JsnC0+iFZ/Guv44+9CI2LEAcuQ5KxySnfgzv6tehfASRxCSHX0bd/j5m6phzwD/0EuruuZRUchM9c8bBicUp1NpVbLaMGT+A6NXR808j2lv4698iOXLWzaWAnelnqHoa79b3MOUZF+uyfQfCgmNdCoHsNRAmcb/PVRD9Jur29/fo6KY8S1CawEqPZNjH9Laxgw55a0n66yilUFK6XDydwoo2DcYUEjwP6wXYXBkblKE4gy0LR8/vN1D1e47skq86mDbuI9pdt0mMB8jeliOmFKYd/GcS1135WaR0NCSbCpZlFLnNk5dx9mZh2Ym0UxNh9ACEj0C7zZg1pIptV/wAKyRWOCNkgaPcWyH3XPCtFJiJL8LB989olFJOcwm8/PLLe44aOzs73L17FyHEnui4VqvtK5oFPh02435nZo+zM6tWq/zLf/kv+eVf/mX+0l/6S0xNTfGP/tE/4sCBA4/sGp+ZYvYgXZIQ4qE7o62tLS5evMjMzAwnT57kxo0be1Eu+1lSyo893lrL9evXWVpa4sknn2R6evo9xz8Ob8etrS0uNL/M4UKBQ/pfIP0C6NCROUYzRmHdOEJJMDoVkQqsdLtZO4qLTxN3hU4QJkaaBKsjJ0j1cwy1pNXZpeApclkJiaOJW4ubHekIk6kQ667zTJQetjjvyB9eiFGhM8vNlCAeIHpNzNgB5O5dovw4fq+OzRcZ9noknSa5yjRhbxuTySMby+jSHDKOMJkysnaQjDFQqDLVvEd//Cim22Q3M0euvQKdLlGuSmAMVOZRy5cwpRmSI6+iln6AKc+RHP08avkipjhBcvwLqNtvYGqLJMdew7v2dfTiM9jiBLQ2QHrI+hrJiS9SvvJ1KD2F6LXQh19BLZ3D1BaRzU2SxedRG9ex5Wm8299HH3wOhj1Mwf3svevfJjnyimNzFsaJawfwr7+OzZawk8cI2ptQnSQ59hqitYXcvuP+nwpQS+exmYITmZdnXUeauIwuPXvGJWxjEYMWsrUBOkFZl5KQKEUXH5ErMdAQWYNUHn42JAh8/CBIn8XUBURHLjZm0IBujMkUnANIpuICPPeMej2EScXMAx9brEGSce40NnFOIMVJUKEjKkkPEI4gYnLOcksPEF7g2K9xFxHm07+fgMxidT81xjZutjbSfEv1LmyehoCO/BaFFBghsBb09Jdh4ec+9PkaFRohxHvSoo0xe2nRI3egYrG4V9zK5fIDF6jHTQAZpYI87DU+jZTpl156id/7vd97bOf/zBSzB10Paml1P+3+9OnTzM3NAY8moPOjjr+fJXn27Nn33SCfRHT9QcXMWsvt27e5efNmKi/4cVj9I9jrfwZkFeQ8IrFYadMHXrqgRekG6O86pqebCeOKmdAJWIsiQZvY+d8lfQa9Id3egGJxjEy24F4sw64LzpSBe8npBNVp4iV9GJuHQQv6DQcnRj1kaw1TmEJ2d8BabO2w69yqi4j6LklYIko89HBAfvYUftxBT51ENtcxkyfw1q+iq4fw1q+QTB5DRl3HsPQyhIMW+AG59hrR3Gni+jrEEYPtuqOgV49T2LmBGPbQB15Abt2GnXvo2TPI+grsrqIPvIDacBq2+MQX8W5+BzNx2LnrN9awYQG5fYeN2mmmNm9hJ48g6+voxeeQa29jyzN4q1fQc6eRjTXM1HG8q99ELz6NzTuyR3LgebzLv4eZOYkp1pBRn+TIWYi7hEvnSHLOhkt265jcmJvnDVqIfgtTnIL8GGLnNururnPHnziEzVWcS0t3N3W3ENjiNNbPOIcMAfFwQNxuUSgWyViDtYYkioiSPvH8CqY2JL4wg6+yBL6PlCmZw2ggQWgNMsF4eUfw6G4jW+vYXA2br9HPTFKUnrsvogHQd7ZaSd+dQ3hOQhIPMSpwtlY442OCbAp9awhyEPcgyI3sglMXG7vXhTkqrkx5PC6uJuU1pabUo+5MoBf/jzDzkx/5fH1Y1ySlpFKpUKlUOHz4MFEU7YmO33rrLYwx73Gv/ygfxMfdmY3eTQ97jU6n89iL2eNef+CK2YMUoyiKuHTpEt1u9320+09STD7u+Farxblz5z6SJfkoYcYkSXjrrbdoNBq89NJLezAJs2ch/7vY8z8N9hJ4p5yv4sjSQeJmWyZxjDfhdnGO0C8QZjSHkFjho7EY4dPp9IgHA8aKeZRnYdh0c4uwAAGIQQ/R2wEZYDIlTD9y87OgAJkCtLfAGkxxxqVE+zlskHfzs0wFug2EHjKIIUx2yE4dwWuvYUqzrpAVJ5H9Fnb6FKrXxM4+gbd5Ez22iFp9i2T6FNK3LhfNGsKVS+ixw3imSXbyBKxfR29dZ7u0SLazhbf0NrY6T2BjZGcHU6ghkgjR2sSMH0a0tlAbN13Xdfc8dtjHVOddQcuOUVq9SXz4WfyNa9jyNGr9GsnME46VWJlDXfs2+sgrThM3/xRy4yYoHz1zEhH1SI6/htxdwbv+HZJjryK7u9gwT//QK5itO8itJcz4AWRnB7F7D1OawFQWXNcSD7GFSZKJI2Atcvcecv0qQmtsroIZm4cgBBMhd+8hhh0noDdOaqEGIY72avCODsk800OMJVhtsYs7RD8o0rtSwvh5VK6Eny3h58aQgzaitYHSMaY8jcmPI7Kp/jAljMjeDgShk08MmqkUJLVTS2KE8p0mTkjXsWUq4OVg2HKzUzwwxgm7R+nQNgJSOFG5YmklgEhdPNwM2GKdz2IqKTBkMUf/c6ie+djnyxjzQAhREARMT08zPT2NtZZOp8POzg4bGxtcu3aNbDa7lxRdqVTe0yU9bgLI6N24H5jxcTl/fFrrM1PMHpSM8XHF7OMKyojev9/1YTDh6uoqly9f5tChQx9JLnlUMGOv1+PcuXN4nvfBwuvyJJz9Gnz3P8IOv43wprC25OYHltRxPEh32p57CbkZuevchMIKDysNRmp2Gx3AozI5hxLCJffq2DEJkxYgnWu5n0VEXeSg5eYb+VkYtt18LFOGJHYv7fy4O7brvA9FfRmNZBAZMlGdzOwpxwAcm0Vu3sTmq66LCvOIfgebKTgSwsQRVDTAzpzG37hOMn4EtXkTPXGMxMsiO00SY1AbN9DTJwmaa0y2VxhOHUN3WySdOgNtUMrHSwQBGhnmEIMuJldGxBnU2jWnEVu/hly/jpk+jmxv0c/WqN45hzn8PGLnLqY0g3frDZJDz7viuPA03lu/R3Li8262VTsEJsF7+6skJ7/gZAXlaZLxA6g75xzsqkL87gqDoIiePeZYmkmMqcwjutuo1SvY3Bh66hiE0pkNC4EtT2Mmjjg2YjRwWrBhK6XaW0xYgkyJSEh6/QFetYqY30WeWYaMQMgMJlEQGEgE4WuG4NkWyfct5maHZDem5RcR+RJ+dpJQaFQK6WGts6+KeyQyxOSLKJ040hE4zaPRacZaHpTnRPKpRo2466DRsOQkG0EWsM7dXgZufqs8rE4cLM7Iesu9N0bG91aRQp4KKw1alLCnfxWK0zzI2k/XJISgWCxSLBb3fBDr9To7OztcvXqVKIqoVCp7xS1JksfemY1m8w+zer3eA5lGfJbXZ6aYPej6KEurEZ59+PDhD6XdP4rO7P5iZIzh6tWrrKys8Mwzz3ws7f5RwIwjY+LRHPBDb9wggNf+GXz3/044/J+RXh9rn0ihHuugoNGQ3Bi3q7WpX13KCtPaEEcxmTCglC8iROrWj3I0aZVx7MGho987xmAJEwbQ7iAGdazv7JNEe8PRwIuTjo2nY8iNIXaWiLwCrV6fjI2Ixw6TG3ZcYnI8wFZm3u0e/Zybw1mBaGxA3rm6i7CImT6BGvawtYN4d88zmD7FIEqQhSqGId6N7xAfeB4Z5PHbO/jZIngexs9hGuskg5iGKpBpriDDPDJXJBACU5lxRWzqGHJnGbV0Ab34NLJ1Bz15FP/qt4iPv+o0bDOn8N/+KsnJH0EMOyTHX8W7/l3M1BFsrgRSkZz6Et711zHji9gw70gkh15E9uvIzdvElTkyjU1k0sbUFjGFcWS/ifXzJIvPQRKjbr2BMDGmOIGZOAhCOCG4TMMzw6KDH5Uz0xXWOn3XoEuwsIv36m1soBFSY4cClIEkDeLUnvt9CN6P1OGpEP/iOMFOicgqhpFmOGiTiXeRfgaqC/ileWTcQegBkEnz0/Lufohj12Upz3VqoojNVlI5SAx+3n02pcAvuHP4oSMc+X4aqhm47ky5WZsL03QwuRXvFjhrBSQRSTAGT/5VyFce+Pl6FBCg53lMTEwwMTGxF6tyf6CmMYZ79+4RxzHVavUTkdE+aO238xvpzP4gr89UMfuotOnR+qDObOR2v7GxwbPPPrtnqPmgxz/Mur8YDYdDLly4QBRFnD179oFuhk8CMwohqNfr3Llz56ONiX94vfzXufHbASfjf4hR30PKo2AnnCDWGlfIZApBCeWE1Ah6gyHdbg8lBOVCzkFJex6OxrVxQoLwnTExwLAHwy4qjoi9HCZTcS/iaOCcP5LY6cr8EKsCZHOdXlil125RzGWJVA2vW8dUJhCDjrsnvNB1MdkKYtDBVg8g+i307ClkfRVbnESuvIOtLrgYm0yF/vQp9OZdgrFpco0lktlT6Lkn3Lxt8jD4GazwEXEP2d6FycNk6ytke1tE08dgZwldX2M3rBKaFiqskFl1rh7SC1E3v0tcOgJGoxefwX/r90lOfxHRa5EceQXv4r8lOf0lRDJEH34BsbOM3F1BL55xM7PjryJ2llGr10gOPI3avIUpT5EcfA6xs+IQu/Is6u4FEB5m5hi2MIEYtkEI9PyTaXfaRG7ddo4nSOz4Avg5xyasX3fwItJBy8ci1Be6BIG7/8XQQwjjSBrCOCGyTjeAFjDSzaAKGvn5FeTmKv75kGxzAj0+RZyMo/sNomaDtpDk6COthxYeXtKBJHEieeUjojaW0EHSSkG/7jSLMnQ/My+DtdrpJL2Mo+WrwLEsPW9PVjIKoRXYPfNsZzHqmLo23kQXjsFz/50zNn6I9ajnWUII8vk8+XyehYUFtNZ84xvfQCnF7du39wI1R11bsVj8xKLl/VL//7CY/TtYP1yMfjgH7ONC6D5pMRvBhM1mk3PnzlGpVHjuueceeIe1X5hRa83u7i6DwYAXXniBsbGxhzo+qv1xdvxXmdv8LzHybaSawJqjYPw9pqNLqXYQY6fdotcdkMtnifs9547x7sAtdVtwWViQEkZU6IpE4GF1Ez/eQg6ymKCI8NLZmPAxmTFEex1hLU1VRrfqlEtFVLYEm3domRDWlwiUQBQn8XfuYsYPp93REeTqFUd7317GVhecL+PiM4jdFWyhhl06Tz8zQb46ix+EmKlj+LfeQB94BiYPI4cDrPRQO0skk0eRVuDd+D7x4RdQcpvwzvdJjp4laK6TbWzQnzyGaW3TsgHB3XfQlRnC6mFqK5cxx18FHZEcexXvwr8lOfNjiGGP5PSX8K58C33waSDG1hawY7N4175LcvQV5M4qpjRNMjaHXLsGuQqyuQW7qyTlWXqEZOIhZmwRmx9DrVx25I/xRUxtETHsIDq7oDzMxDFskAEdIwdtGLQdfBwUMLkqnOojTm0jsmDiDInUeARIZTFaQmggVk6pMSIARTHCDiFKENaD0MeOefCjbg4qlyDcmEZon5yMifNjJFEG1dqi1WgQCI2SA0KGqDALQd55O/a2sYVxV8giR/DAz2FN7FivIycaKZ1J8F7yg02JIGnxkoK9lGhPYulhoyX05B+Hp371oZ8vePzkjFHHdOjQIXK5HIPBYE+0vbS0hJRyj/pfrVb3Rf/fL1vycVPzP431B7KYjWDG7e1tLly48ME5YB9x/CftzKIo4nvf+x5Hjx7l4MGDD7Wb2g/MOBgMOHfuHEmSMDk5+dCFDNwu0YyfgSPfhNf/OCa+gQyaoOawZiG1EJJYY2i0mujhkNp4DR1r4l7XvThI/RxtKrhWpFR+C2KISBKIhwjhYZVH5JWw0ndO6EJhs1WIuo7NGJZpdnrIqE6pWkUiEbv38CpzVFsbxCqkRxaxvUqUH6ewvYocWyRo7mDLs04cHeaRa+842HLzFqa6SK++xaBylNpwG3wfubWEHZtHH3rRGQlXFxDDLpSnYWyO4Mb3iA+9gJ7NELz9NaJjn8PMnsa/9PvEpz6HUAG5e+fQR18h22tihiGms0M3LGOrRxm78k16B54n1H2S0z+Kd+krJKe/4ATWJz+HWrmC9TLYwhgEWZLTX0ItXcAWxpH1VQiymLknHANx0MWOzRLeveTCUQ8/4+C3eIiZOIzJFpHtTdTNNxA6xswcd0SK1iZSR0747AWYXAUb+HBkDbm4jMj2sZGbW9lEIqVGmgSUQcQCvARiwBMuF8+XWJsBz0JiERg3R7UWIQxWdVGHb2KPrGE3J+BGBi8Z4mULDNoNxqo1bHeHKB7QtgI97JG1dWShQhCWUUm85+0oTOK0hipw3Vf6q8UDYqeJtDadizlyh1UpG1eAkEPQdzGmiT70/4AjH069/7j1uIvZiDY/ukYmk2Fubo65ubk9+v/Ozg737t3j7bff3qP/12o1SqXSA322/RazT4Oa/7jXZ6qYPQjMOJqZ3bhx4320+wdZn6SYGWNYWloiiiJefPHFDwzv/Lj1sDBjvV7n3LlzTExMUKvV3mcJ89DXLVXhx74GX/uPMb2vI4I7CH8b4kPEpkRjp4ECauPjSBRaG8cUQ7n/pDMnFpg9AxEhpEse9nDzs6iPivv4cQdU2Ymoh13oNwFBnBunu7mK8jzyk3PIzg5EA2cd1d7FFqr4XpZw2EFXT5JpbjFQFXR9l7aQ+HpAEBTxwhyecvlrIBncu4pQHrUwA9PHEP0OZvoY6vY59MQhV8iSBFscR91+E73wFPrQc/g3vos+/Dz6xOfw71xAz58hPn4W/9p3iQ49j517Ev+tr5Kc+gJKKBQwlgzYsZL+4nPkls5THz+Gsi3EwZcoXf8+ZuEJRKeBnjmF6Owi129jZo8h6+skB55BtjYRzaYL27x9DjNzDD15GNlrEFUX6RmoXv46NpNDH3zGEXT6LQgKJEdeAgyqtYXYWUbEfUxpEpspIUQHdfAczLURBY2NU3ZqIhFaIrVIUxR02oUJSHCOJhow0vl7GuucOmzqnN8bIkTiwi5VBoidkHxyCzGZYFtZzPYUar3vAlKLLr08N+yQSJ9YZ4iihEG7jg0yBJksgS/xg9CJvBOD9VMDYc9H2CTVP7KnF7Ox+xojsXSR/jJG75CYAvaZ34DJp/f1bIzWp+GYDx/MNLyf/n/kyJH30P8vXbr0wPT//RQza+0fdmb/rtb6+jpCCF5++eWHppPut5gNBgPOnz9PHMcopfZVyB72+vfu3ePKlSscP36cxcVFbt++/YnII3sbBc+DH/un8O2/jN36n8HvYMRl+lGGILtIMTuOFALixDlJWDdgdzO2dI9sEoQ2bohvrAv2FBIrPWyQx8iApDVI/fja4BchCIgbG/TaG6jiOPlcDtFYd07vxTKy33Zu+cmIKj+B2l5CFsYI+h0ILImXwTY36IZVvJ01ouIkGTOkR55M1iNfriF3l7Fbdx3zMY5IDr+I2rqD8QJob0NpCn3oOdT176Hnn0AfO4tcuYodX8QceBq1dQ9TmSI5+gr+3Uvo6WNEx18luPQVolOvIcIiQjfI9JuE+Rz25KvUbp8jmjhC0muzM3mK/OptbKaA6naQY9PYg8+g7l7CzJ3Eu/sWeuaYc+2or2MmDiFXriCFRC8+ibEK2Wujj76EFRJ16xwiHqIXn8CGIWpnBYKMI3lUZlyXHG4jT1+Dag/CBJI8RglnxCsM+GCMwPoJOrJIX4JW4Jn0V9zPFAv9CGGGrqiRgUBivaLrnHTq4SlxxU44/aIIWsjFIbnZGDUwsB1g6lVEUMJTHl6/TrZcxlIm7reIdUwnAtvu4GUy+L5HgEQplRYxnZJ+bAoGKBAJYXYX4a8iRAcTxcTqGHzuX0D+wVIvPmp9ljRg+6X/7/d7+EOd2ae8Wq0Wq6urKKX43Oc+ty8j0BHM9zDO+/V6nfPnz1Or1Th48OAnCq17kM7MGMM777zD+vo6zz333F7hfORWWK/+VbjyLL1LfwFr22RzCb53A0wHogWsVAiSvUF7ikW6mYoZOa2nMCM4VmESgTFII9FCYsOK8ymMegzbu7SGmnx1hpxNsN0GpjiF6LeRcR+TG3NkjLjvok+2brtgzOHAQU3FafzGGmbmBGNbt0nmjpJZfpt6Zopi+w6d8gJyZwNRWSCTdJ1x8fYSstfCjC8ghn1sbRF1+03M+AH08bPI1evYksVOHYZeG4HAFGvODd4KzPwp1PYyojRO8uSPE7z1+8RHXybJlDHtDqLThDghOfgc/uoV/NIk2aRPfPBJzO4adOoMBkNMkIPJE+R216E0hVp+x+nBJg4heg1MZQ6yBby3vorIV+mPHXA2X1KgDz0H0kfuLCG37kGQweTHoN9GBW8hXhxiSwJCiTW+61yUhdgi1AAbS4Tn5mJCxdjYOonGUCC8GBuD8ATGBBAqrCyAZ1MHELDJCGLU2Fi7LkkqdztEQ2c6TOC6PJ1A2EQsKNTiLvQFNiphuznoaoiLBNkigTDkjCZRHvGwR6Q13d1NhBe6/LEgIMjFiKCL8NoI2SETdkjiGEyAjhKSzBfgi//QEUoewXrc8S+j5+9R0v+vXLlCHMd79P8oivZNAPnDYvYI10cVlxHtfmxsDCnlvh2t7zcr/jjShrWWu3fvcu3atb3uaDgc7uUe7Yd59HEEkOFwyPnz50mS5H2ElkddzIwxXDEn2ZL/FS+Lv4nUbSwGoVYh3IFkGhFPsBevMVoWrDXpkN53WWpWpMxIRwFHD/G1C4q00qeVKIZDzVgg8EgwQQErfFTXhXcaP4dsrGNVAIUJRGMTU51PX5YhJl9DDjroiUPIXhM9eYS4sUMnN0NZGvyFkwSb9xjkqqi7F9kqLZAzHSgvkOvuIBvbgEVEQ/SRl5B334IkwUwecro1Y50mC+FsmhrrUMy6nLbSpJMeJAn6qR/He+urtCoHCKszznFj2EPsRCQzp5C7ywgE/tZdzMQBqEwSrN8m9j3YukO9NIfXbpGReaSVZN75Oubw89hsgNBDkuOvEvfaVJYvIAtj6IXTiNYu+AGmPI2dOoxI2si5JcSxHVBgAs/Bvf0B0nawkUAGFhsJRCBcgbNORGhjiTUWa1y0i+um0x8qCpI0MQGDTQTCxqm/J06KgYIodsoO66Up5rifuVGOUCIkxM4TFM+A30JmG1DDETe0hCQAI5FGEFiPPAJrNUYkaD3E2oQYd49Ja5HGwyYJJjLoRJJM/Kfwyn+9r2fhw9bjNgG+3y7rk6yPov/X63WEEFy5coVarcbY2NgDvef+cGb2KSxjDG+//fYe7b7f77OxsbHv8z1oMdNac/nyZXZ2dt7DHhzd7A9SDD/s+h8WF34/Q/KFF154H/b9SWn99x8bRdEebPrSH/1PyCT/Ifzen8AMriEChVADhFpC5tfx+nmsHHfzJuleYEIqN6QXwlG73SfESmdkbEVAIntYK+nubmEMVMsVZFjARgMXhYJwtlaDNqK96XLJ+h3oNbFjc4h+K3VLD50DSGkKuXkHW6gxXLtDZKCcy+OHOecuMXmQrLGIzHEm6ptEYRG5cpWd8gL+YIjK5snXV5DtOnrhDLK5iRj0XAekjKP4L78DE4vY6jzy3jvYqUPOZinqg1DE63dpTp1hYvs65HLYUg16PqLbxNu6gx4/iO03kN0WYv0mdmwGPXccb/MuTB5iaukCwwNPE8cxcbdJq3KE6rXvIzyf6NCz+FEfhEd97hnGAom6exmsxcyeQLKMOLwDizFWBM7NHuv0YcKAyWCC0GmxlMV6Cis0wgqscV21RYM0WB0glPMsRIIlAW2cV6aRjvwh8i7uxYJIEoTRWOs7Bw7tft4kiStQBI4sb6wriEI5tymtnQJMKNdda+M+q+g7kTMidbS3CCtR1qCUxGoPayxaW4yOiGKNNZahDtk58F8x9vyf5FH7aHwawZyP+vw/TP+/fv063W4XpRQ3b96k3+9TLpf3iCSFQuF9xbTf72OMeeCA4k+6fvqnf5qf/dmf5ed//ucf6Xk/08Ws3+9z/vx5gL0uZXV19RNT64UQH3mOEd1fSsnZs2ffE+t9Pza93+t/0LEjB5EjR45w6NChRy74vn9m1m63efPNNymVSvfJCrLwx78C/9ufwnZ+BxGEWM8i6ZMrtJDZAXYwg0gm3Mtyz/pHMuKaORGsQRiB0I4gstMdIP0ClXwOGfWwnR3ntJ6rIYddZL+BVQE2V0W2tyHIY3IVZEo7t4Csr2Cri6jNO5j8GL2dDUiG5CvT+K1NTDCH3LiNGV9EdOvY0iRU5wiERPgek/U1hmMLmNYuu/lZMu0NvFuXoDZHYAUiP4ZcvwH5GmbxSeSNN6A6i1k8g7r5BmbyCLYwwXD9NgOZoSoG2BNnkbfPg46w5SmsCpHtbbzVa+iZoxg/j6yvIZqbiKZ05I7ODvHikwRLF/ALVczscXKDDnHmDHESk3/nWwzzNQaVWfxBGzM2jj38DGJ6BTF7CVnsYUUGi0BGTUeICATYDDZUzkA6MWAdO1GoCBIFUiO0RCiNHYKSsWM/KgMJjr1IxrnkyxLWWCSx666sBeM7wqp2Gi8SEHGM9ZWLiTHSFUJhsIkEX7nfK+m6QUgh6TQUNnWYwYzgaUjV+1jrCqy0AmsESlikCFFC09J5Lmd+lUQfZvD1r+9Ba7VajVwu94k7nk+DAPK4HfMB8vk8x44d49ixY/T7/T0iyYfR/7vd7t5xj3v9k3/yT/jd3/1dfvZnf/aRn/szVczuvxk/jHb/Se2oRuf4sGI2ctf4MLr//Z3ZftYPw4zGGK5du8by8vLHOog8Cphxc3OTCxcucPDgQY4ePfreF4BS8Mf+MXz7v8Hc/btIA1pITGKwpg/hDUS4gh3OYmPXqTrnhdTayuj0pQXJYICnh2R8SS5XBKnQmQroCDnsI4Y9p4MKC4j2DjJpYooTiDhCtnew2SKi13IFsHYQ0doiKU3RbrVRKiQ3dQDV76DnTiJbW+i506jN25jaPPLe25jZE4j6GnZsHiYyBDqBXJ7s9m2ixafR7V3ibpdo2EHiMswK2zedg//RF5F333KZaEdfRt58k76fp5+rUomayMIkYnsFs/g0cvUqIlrGVGcx5RkEG6iVa9jxRez4AqKxgfUz+Ne+S3LsJRh2SGZPuQTpi79PcvIsvtIEfg775JdQjQ1Ka9cYLBaIn6gTTLYhJ7Ayi/FziETDEJc7FwSOXh9pRKvtkOAEhOc6LzKuw3FCeA+LdA7yQiL8ECETwBEr0BKRRFic7tAa3LUgZbN6EA/AxohApjZT4t2fufJToXXiilM6ThUIl39HGp4pRkXLpr9XezNXq1M026R2awasNhBr4uBJ1o7/GoUgw6lTp+j1euzs7LCzs8OtW7cIgmDvBf0g0NoHrU+jmH0awZz3j2Cy2eyH0v8vX77MX/trf40TJ04wOTn52BOwd3d3+eVf/mWOHz/+WM7/mSpm4G7iW7ducevWrQ+k3T+oa/5HrQ8qZtZa7ty5w40bNz7SXWPke7bfz3B/dxVFERcuXGA4HD6Qg8ijcA9ZXl5+XyzN+9ar/zXUnsOc+/MghlhtsEniKPiyD8EthOdDPAnDuTRKJn1RCZ/eYECnO8AKn2yu4F5wcYREuLDFTBmrE+Sw45zVM0UMAtnvYIXA5MeQu2uOsVeZRwzaxGGZ9u4WGQWZ6jSyuYUpTyF317DlSWSn7sgU/Q5m4UlXyCozyKULmIUziKjjYlxkQLB8GTN7nIyU6NoMbN7BrF5hp3qQbHOD8Or3GSyeIdPaQNx8k+3KQQq7d6naTez8SdhawhaqyK276JnjyK0l5OYSdmwGW5kGoRA7q4gggx5fQHYbmMPP4l/8PfSJV1z8iZ8neuJH8G98H1RAsnAaOVjFe7aP/qkCodfCk0OMDjHGIrsNrJCYjIcll2bVWVc4lMDaEgRgE4VVBqFTSFG4rklY+67jfCzBE1irUt9EgYgTV9SMQfjKuXUo66yl4r4TTYtsqjlzllFgsaOikVhXzPYKkkBoixXKcYe0dl1ZakGFTuOI0GlMjCsiRrti52y1DGaoSWp/FH70f8LeuoVMN7K5XG4vXFNrTaPRYGdnhxs3bjAYDPbVtX0aJsCfRjDn/UjS/euH6f+9Xo+f+7mf47d+67eo1+tMTU3xYz/2Y3z5y1/mp37qpx7cYegB1y//8i/zJ/7En6Df7z/S847WZ6qYRVHEuXPn6HQ6H0q7/6Si5w86x4e6z3/E8Z+0QxpBfcVikVdeeeWBdpL7LWZaa7a2tuj3+w8uZzjx70H5OMlX/gOS/jr4CqtA2DTUU8RYfxnhryPiCjaZBJOl3RvQGwyoVCeo1xsOUrQCYQ0iHkLcQ9gBSOUYeVGM7NWdSDhbhkHHEUFKE+4lPGgzwGe4uUzeE/jlOUezHz+AWr2OqUwhNu5AmEVs33NBjtEAWxxHaI058DRyZxlTmULePo9ZOIOdPooY9AGBt3oFs/AEqrHJxMZNhoeeImnuom5fYru6iO+VKK1dwRx9HprryJvnMEeeR+wsY3Ml1PotzNRhqK8hdtcgW3KfXfmQxHg33kQffR4x7KLPfBF18xw2zGJmj6EGXfSxZxDzK/ilb2GrGWxg8LQm0R42LCKweCaBTAZjA0TcR0V1B+x6CiNyqDBlFg4ihEndXIRAJDgoUQPSIiKQMkEkFuF1HSXf91xGmBe61OdYQDJ0YZheiLWhs7oyKasxjpwge8RejJN0Zpo6dRjhrmdd1yUSncKN9t2OK7XQEnjvdmUGwDhyiBUYozGxIjn85+GFvwh8uKv9SCozYv2Ourbd3d29rm0ErX1U12aMeazdyacBMz6MziyXy/Fn/syf4emnn+bnf/7n+df/+l/zO7/zO/zjf/yPWVpa4td+7dce2ef62te+xle/+lW+//3v80u/9EuP7Lz3r89UMdvc3ATcfOzDbqpHDTN2u13OnTtHEAQf7D7/Mcfv59r9fp/vfOc7H+uw/8NrP8VsMBjw5ptvkiTJnpPAA6/p49if+ga7/+wLFPo7iIzvdtdSONEtEkQM3jaMbTPseZh4jFruICo1L+522oRBgKdC5xno5bA6dnR83XTdRmEcEQ9dEjQCW55B9FqAoGN82LpDtlDGL9YQ7W3MxGFEewdTm0MYID/mYl/aO9gwj9xexiCcmXG+iqlMgzGYhSeQd9/CzJ92Ba/sIF11+ZskJ15BBnnCtDjFQZbs1gqmMskgkye4cZ7t2kFy2XFyl76OfuI1VHPDdWgrVzEzx8ALoN9Brt3CTB1ERAP0winU+d9FP/2jiEEXffApSFoo+XXsj4xD2HPGwH4RBjGiPSTJ+KgkRrQjrB9gRAYhY6S1QAi5DNYosBFi0McONM581yJ8H2wGEVgnrdiL8kkg8DEixliQgXRsRRG7+ZaOnD8nqUDejuBBx0y0SYxVeawKXWEzrsDhyZTdOjL5xRVQqxxEiEQMrTMRNppU0Aap276rbRorfNfxWYtNErQO0c//TTj2U3u344MSNB60a6tWq+Tz+b3n79PQmX0aMON+U6aff/55XnjhBX71V3/1Y80rHmYNBgN+8Rd/kb/1t/7WY42Z+UwVs/n5eaampj7y5T4qJPulxt9/jq2tLS5cuMDc3BwnTpx44Bt5vzCjtZaNjQ263S7PPvssU1NTD3X8wxazRqPBuXPnGB8fJ5fL0W63H/YjIwpF3l7475hN/j9427+FCQKEdK4gI9s8A0RxhJAJ5ZlNhKljh0UqY0WGrQGdTgtpwfMD/CCDH+YgN+ZeiIMOcriL9bOY7Bii13S6q7BAt9lEtFYIJxbwhEREPUxtAdlpOAd67ZKQTaaEHLQcA7LXQs+fRDa3nY/j8jvY6jyiuYEpT2IOPIVo72JzZdTNcyQHnsIeeR619DZm7jh2fIG4vk0nMRRKNQJfOe/A3EmqWyv0SpM0a4cov/m71A+/QG7QwytO4t15C7N4CqECbNRH3byAPvK0o/M//eOom1/BfH4ROV+HgsYwhhjsQiKxIkQmEcbziFQOT2ukEFgVIJKB+3tKYjN5rPWQOkIkKZkizGPwQCToSGCJsUmCBKSxCCWQdgQzpq4fWmB1+oNDOMsqkWATD+tJhFDO2zEZgMiCChFWYo1ws1FhEQSugiW4X3XKYLQCIgNC7gVB2/Qarnsz97FfU7gxNa+21mAT0ExgfvJ/herie+7F/cCAH9S1jWjst27dwvf9vf//uONZPo3ObL8p0/cXdfhomdTDrr/6V/8qzz33HF/+8pcf2Tk/aH2mipkQ4mP/EUcQwSfBt6WUrK2tsbOzk6YzP1yOz35gxjiOuXjxIq1Wi1wu99CFDB6umK2srPD2229z7NgxDhw4wN27d/cFUe7tWn/y/w1v/o/Yt/8W+BohPZCWxFriZIjyJIGnsIlIu4BdwultshMBpl8iblSIOzDotOk2GgRKojIF/GwBFUjkoAPDHQgLaOnT21hGJBGZmWN4UccVzVwVWd/EhjnodxG9JrY6j1q/iZk8hFy+gpk+jFy9hZ1cRHQbjoLf3nWF7fYFzMRBR4BAoA8+7WDAA2cws8cQ3RY9qzDdFoWJBQI0tHawY7MuUaA8SWHQxVbGSUpnqb39TXYPvwidNiJbo3TlDaKDT+KHBfSBM6jtb2BePYis1bFfKiA6y64r0aFjewZlBANEf4BRWWzUIbAeIptzFk6RBeFhcyFo6Qr2wCI8IJPDWB+BRg77IDXSKJCuONjYgtZYo13tMG7z58A9i9AeVvpYT7k8O6FhmCCSvtP6SR9hHRsRjdORpQkJrsPC/fkI0gRXsBIBQYBNnLiatDtL/zKMNvwW0hwXrHZzPRtb4uAU/PS/gPD9c59HQZ0fdW3z8/N7Xdvu7i43b96k1+vR6/Ww1lKr1d73gv+k69OCGT9rKdO/8Ru/wdbW1t57ttfr8c//+T/nBz/4AX/zb/7NR3adz1Qxe5B1v05sP8UsjmM6nQ7W2n3ZYcHDd2adTodz586RzWY5ffo0V69efehrjq77cQXJWsvVq1dZXl5+TxzOfudtowfDWguv/EWoPon91p8D2SUBEh3h+Rl8hdvtO0tzhHQwlJEaUdglKNQJbYAdFElaJaK6Iul3GbQaCM9HZUpk/Dyq16Hdc0zH4lgGNWxhwzwWidxdcVq0bgPiIXZ8EbG7hpk6jNhdd7Dj7iZkC8i1O9hcEbVyDVObdz6Jh591hJF8FXHvbezkQfSxF5GbdzHlKfqdNgMvT2l8Hn/1GubAk1CSyLuXMQefAgRC9hG9NiqTRz/9o1QvfIXkyS+S9Lv0agfIed9leLSMX40hzKNaN7B+BYYx5LIQCUS7ic0VEZ0OZEJ0JofpRnjCR2QyiHoLQrBBAUsGYRwUaFUBSgqTgNBDZNQHadICIrFSYVEIzyIMCM86QojUGC2wJBgtENKgrEJoi0wirE1Smr3vao12HZY1BuIY/BDnhzW6ydK5qcZBzkJCEjvLKQ0kxpXMxNynQ/TSuZh15A6kK7oG0K5WJhN/HL78tz/0XnzQJOgHXfd3bceOHeONN94gm83SaDS4ffv2e7q2/TIk71+fZZjxcdLyv/GNb7wHFfqVX/kVXnzxRf7kn/yTj/Q6n6li9iA36ujlmiTJQ0ckdDod3nzzTQAWFxf3jd8+zMxsc3OTixcvsrCwwPHjx2k0Gp+YPPJhEGscx1y4cIF+v/8+duQPi6YfdN0/TwDg+E9gK79D81/8e/h6g2wmQCFcJyAEQljXHWjpojzA7cAlGIaITITK7JKdFBDnsb0syZYh7nTotCIilcFXGYq6jxyCKY4jOnXksIcpTyMbG46YUJ1ADNqOit9rY8uTrhMpjjnndS/jBL/GILotRNRDtpswMY8YDjCHnnGdWnUWXRqn06xjwiK13XuY0knM4hOoy99Cn3jRff32t9EnX8Hmx5A7q07GUG5g/v1TeIOvIBcnCP0YZJ5ca4eEMiaKSbIFvFYbwhAZD7Aqi81VEXEHpI/pOgNflSkC0sGmYR6hPES/iYg0ZAKsV3BWUsnQRbIoz8W+CIEIjStwVju/TGHBuLRljEYaizQmNfhwOi5tAZsgTKp5FhIhBdIIF82ifKzyUz2YSw8TSepWb4Uz/CUlgCgJeC6/zAisTmmNVsAoE9qa1JTaOYBYDNZIrLZo7aFP/l/h5V/4yHvxcYuahRDUajWmp6f3Yp5GoZoj8fGouO2na/usEUBGq9PpPNZiNj8/T6/X2/t9Pp+nVqt9ZO7kftZnqpg9yBJC7Iuev76+zqVLlzhw4ADD4fATfYYHgRnvlxicOXOGmZkZYP/zttGxo3P/8IPU7XZ58803yWazvPLKK+8j0LzHaPgh1gj6HR2bJAkXlxt0Dv4PvLT+3yP6b7nPJEHKtKCNctFsmg4tHIolsE7AO3oZyhai1CIog0okqqkp6jxJJ0e7k8d0+mS6d5FBliBbwW9tYfMVB4H1mthcGbm7jvVDiBPnGFKaQGwvuzlZZxdTmnKBnqVJ19k1d0DHiF4bc+hZ7M4KrX6bXK+BN7mIOfIM6vK30QeeQD/5mvv60Cn0q0+g6l/FPDGHzcUIuwwZp/OyYgzZ2MYWy2AstlDFazaw+SLYGJ0twXCAtgmInutU8llsEoEGmc2h2g2nxSrlEVJDYrFeHusHoIfIfgsRWWzWx8oAkWiE7jr/Rc8ijUIo60TLypJWN6xxXppoC75AapcBJlUAvsTEwhFyel209dGhhxBZVMo+dFZWbgY2YiRiFcJojJSAj4hduKs1EqEjF9uiDWn0c6otS4kiJiWKGIHRCVqUMJ//23DkRz72XnzUndkHnf9+PevIoX4kPh4xJEdd2/3i4wfp2j4Nndl+Z2afppXV3/27f/exnPcPXDGDh+uMrLVcv36dpaUlnnrqKaampnjnnXc+cabZRx2fJAmXLl2i2Wy+D8r8pLR+eP8ObyQwn5+f5/jx4x/4wD8KwXW/3+fNN9/E931e+dKX8LyfIPn//gJy5V+hPJuSB1KvP9eSuWiRdI4jwFGvhVMYiTSGRBtNoi1BOUSqLn6tTc5qrA2JoxDbjoi7kp43htePCIcKUZpCbd2FTBGsRHbrmNoccmsJM3EQuXodM30EtfQWZv4kYusuZnIR0Wtjgzxy7Qb63lWafpGMJ/GPHEOtv4kZG0P/0QXU8C1sxce+kEMNLzqXkrCC7N7DenmQOeh10tlOjClWka1dbLEEeogtVKHbgmwWNexhwzzChtikh1EBotHAZLKOHTg0rhuzHmK7DoHChGWEBskAqz1MWARfIWyCSIYpxAfIAKtcWgFol0lmbaojA5RIc8Pdn2urESZKc+c0UmYdC1OGiCTGaIFJNNZEoBQCH6kNQqVwoXCieCvSyBibMhZjFydjtefSglDv2mgJixklKxjAON1iIuexX/4NmDrwQPfh4+7MPur82WyW+fl55ufnMcbsMSRv3brF5cuXH6hr+6x2Zv97SJmGz1gxe9Bd14MWsyiKuHjx4h7sNtp9SCk/Eb3/o7qrXq/Hm2++SRAEvPrqq++DQj9JUflhX0lrLUtLS1y/fv1jc90+qeC62Wxy9epVpqamOHny5LuWYH/0/4X59inEpf/eJYZI7TRNMnWOsMYZzrozuV0+I4GsR6KHYCyB7yFMjNAq9RRUoGMCfwgTimBSYvSKCzhEwPAq8VwWaTdRVmL8AmJ4BbuYRwyvY+d8RHQTOxMio0swGyJ638AeGEOaDvpUiIm7jIWbSKlBCuwzGURv1UGytRwi6UMcY4I8YjAEPcRka8heHetbyBRd1xf4iMEAmx+HZh0KeUTUwWTLLsfN8xCdFvh58AvYqIfxCs6H0Q6IvSI6ShBiiAjLSGmQnVaavVYABKI3cJCfwLnUCx+hEmwiXZdmdfpvTSpCNq7YkP4qLVo7uyjpZ1w6s41T1w7jNh2JRgmQKouQEmMNWlu01ojU41GowFnC6ST9uaaei0jnEalxDEdI/SCdVFsY0s5MYyJDXHkWfvqfwgNIYUbr0+zMPmqNLKHu79pGDMk7d+7ged4Hdm379XN9mM+/n4Lf6XSoVquP6VN9euszVcwedI0COj9qtVotzp07R7FY5OzZs++5iTzP+0RQ44d1VyMrrJmZGU6ePPmBN9UI7tvPLu3++dXIgHlra4sXX3yRSqXyscfut5hZa7l8+TInTpxgYWFh7/qj74fP/wJm6iT2//efI1XfvXOlTOGplNGWRsg4+yuB/f+z9+Zxdtbl3f/7e99nnX0mk8kCISvZl1kyISCIFhUQAhFprdqi2FZpWR4UsJWntI9LbWupxR9W0arwWK1Pq0QimyIQIgqiSWYm+zLZZzKZfT/bvXx/f3zP9+bMZJYzZ86ZiZLP68WLV5Kz3Ge7r/u6rs8iXBJWAgyTgC+odm2uVKQDN/nZ+vyABQkHYUgMX8CLmHHDSq8miZPAwCd7cfODmG4nIs+vXP2FodY2CCRxRIkf4fbgSgcR78dXUIghXVVs4lGI9SPzCsGyEPE4BJI7t2RgJI6LiMRUrE10ABIDyEA+Ij6IDAQQsT7c/BJEdBAZ9CP6eyBUAm5c3T8ex40qWy2fK5BmHsIUBPp7lT1VXhg3buMIie0PgFmALxHDcCyl+woaSMdE2FFEol+ZKyfP7cLvU12RzwXXVN2vg0cQcbFxXQNfQHVMQhMzEgkQDtIXRppvkk3AUJR+w49wwDUFriNxEwlsqbSGprSV8b4wkyxNcB21M1VfVIHEBOkgpYG0HWUbueiP4T3/nNH38Hykzg+3jNJd2/Hjx72uraysjHg8Pqo7RzagL7Az6cwuueSS8W94nuO8K2bppE2P15lp095FixaxaNGic67mJrO3Gun+qR3SWFZY+tghsx+O3l/FYjEaGhpwXfccI+SxjnmixUyPaB3HYfny5VxyySVeITsnyuLSa5AlP8f58R9hJppwDamKmhDq3KqWZAhX4iKJ2xY+U+AXpiLHuXh2WOqs6CIStmLXmQE1mYzHVMdmhjAcGyl8CEzMRBzXF0RE49gCsBKY0kUGQhh2DIJ5iERUOW+4Elua+AN5GLGYIovEo8hwPsgEDAxAMF+dnBNJNbDP0MseQBUlAvmIRAw5OIAbLkDEIkh/CKO/DzevGGENQiCM6OtE5peq6ZqMg5mHf6AXmV+kio90cAtKEJaD0d+DMAIYgXw1qnRtHPxYBghHYFoOhnTULtKvkgmE6SqyjbBTfA99COEiDT+YNlayOPl9JiKRACeiWB++ENKfr/ZcTpK8Y8sk3R61ZzOUPEDYEp90wQwiXYkrwXUFlqVaMQMzSe4QKhBUh7g6rlqd2TauY2LX/h2s/8iEvoca50tnNhZSuzZgSNfW3d1Nb28vsVjMY0hm03FkrCTrsaB1Zr/rOO+KWToYrZi5rsuhQ4dobm4e07R3spZYpmmSSCSAoVEx6XRIqXuvTGAYBnV1dcyYMYPVq1en/cWdKAFE7/36+voIBAIUFRXhOM7YmUwzL4aPvoLzwz/G7NyB8Jlqj+baiuFoSBxbYls2voCJLzmaMpKdmsoicRSBwfApYbZjg2upk6oRAtdGuDbSNBGWo7q4QBjTjoM/hGEIcG0cIcCKYwk/vlhE2TUN9uH68gg6CQjno2y5AMNE9CUJGyIIjpXcD0mk6ceIRVUR9QcgngCfCXFbEU+wEP19yIJChB1HBsIY3V24xcUIx0KGC6CvG9fvRwSCmFLghkoxBnoRrlCFz7WQ0kSGZyCcOGJwUI1qQ3kYCQvh2riOD9c0sIRAugYmDkJaShjt+tQuCxNsoUI1hYNwLFwnjumYGEG/InH4QkhDqNBVNylrdqR6n/1BJcS2XZWMgKH0cI5UBQoTYdsgfBgIDAw1ZXQcHFdgJ78fcSeOYZiYCBBCRZ05xTjvfQwWXp72d3A4ztfObCykdm11dXXk5+djGIbXtRUVFXm7tpHiWSYCrTGb6GNc2JlNI0aytNKhlpZljWvam41i5rquZxUlhJhQhwSZue6fPXsWx3G46KKLWLFixYS+tBPpzPTrMk2Tyy+/nF//+tdYlpVeuGAgAB/egrP1ATj23yrc0fAhpIltxXBsB18ggA8VEyJIRoQYJpB0qpACsFWXLgwl6rUthBtH+v1Iw4BYXO25fEGEZSmqvARhOUhfCJ8dR/oKMO04jgjhxm2kyMOwHGwziK+vHxkuQMRiEAoh/T6IxCAQBNtF+k2EZauOqyAP4jEV4hkqUJ2ZMEDaKgIlYGL0dCOLSsCxcfMKMbq6kMWluLaDY4TwOS5GtB+ZV4KwJDJQABKMnm4IB5SWK+qoOJa8InBcReW3JDIYRPhNzFgCnxtTRUhIXFfgmIZidwoTw1QMQoGBtE1s10HIIKbfUGQMzcJx1ehX2AmkL6hE0lhv5pBJqbwTbVcRSwSKgi/ULlPYrsr6lKrTBhOfqlvYEgx8uJZDIoHKIvNVELnx+5ResmxSGWRT0Znl8vGllBQWFjJnzhyWLFlCLBbznP9PnjzpMSj1rm2iXVumRsa/DynTcB4Ws0zGjD09PdTX11NSUkJNTc24S9bJFjPDMIhGo7z22mtUVFSwcuXKtL9E2nV/Ip2ZlJLGxkZOnDiB3+9nzpw5E/7Rpfucvb297Nq1i5kzZ3oFMxwO09DQQFlZmZdwO66H5c3/gvPaUsQb/4RpWCRkAheHYCCkViqO2p9J8aawVgi/slySBooJmVDFzVAnWVf4lGu6dNRJ2HVUrpbpV9lbjgOBICIyCIGQ2l0ZPrDjmIaBYUqk4cN1XRJmCBGLI3x+fL29uPlFGEbQ2xeJgYiKoREC0dmNLCpFyjiitwdZUKp2Ta4LhgXCjwwWI7q6kcWlymswvwTR3Y0TDuEzA6qYmCFEdzcyv1h1Q4bALZihLKsGBxRLMi4R7gDgR4ZCENQuGrbqVn35Kn5FSAwpVWEUNq7jYjsO0jURPhfXERg+A9P0K0mEnVBFX7gIM4z0+5PjQwcpk871KLaisB2kTxkQi6SfosSHcETSxEPZUCmGpOJKuq6LdIQah/oEpvRh4DBYUkvTxn+gs62X2KlfUFpaOsTNfiLIZWeW6R57IhjONAyFQkN2bVrXduLECfbv3z/hri1TUfbvQ8o0nIfFLB2k6syampo4cOAAS5YsYcGCBWmd5CdDjwdFLunu7mblypXMmzcvZ4UFho77Nm7cSF1dXcbi5/Hu19LSwt69e7n00kuH7MfWrVtHJBKho6ODM2fOcPDgQQoLCykvL2fmzJkUFhaO/B5c8RckZiwjvuUjBESCUDiMcJPaJwO1o5FCjQyFAFzViZHcsRlBFfzpOgjXUc2QKQBTETQMU3Vm8YS6nc+PSEQV1TyRwMXEshx8QumqREJ1Xr64MvBFmDiOS8JXgDkwiBUMYroJCORh+IMY/Z24eTMgXIzo6UIWliADJqKrE1k4A+nEMSwL6QNMEzdcitHdjSwqxknYuP4C/ImY2mv58tW4rnAG9PcpskthHsKKIkUQwn5IOMpxI+AH10T09iTHewEI+VXKt1QFHGmoUaKr3jtDGiCEipNLJDBsiUi4uNJQBd4IIIJCeS66asWmilJSDoahKP/+AFL6wEruCIXqmD3xs9YLiiTZI2lRJaTASTi4rkzK3CTxpX+K//rPsTRZILSbfUdHB42NjYRCIe9kXVJSMu6JOJedk76Anq4xpmEYlJaWUlpaOqRr06Ga6XRtmRQzKeWFzmw6oceM+/bt4+zZs1RXV3tGohO5/0Thui4HDhygra2NwsLCjBlA6XaGqbquyy+/nEAgMClbqtE63tTOb926dcycOXPIfswwDAoLCyksLGThwoUkEgk6Ojpob2/n5MmT+Hw+r7CVlZV5P6hoNEpdp4/QZV+nas/nEYlTSL+BIfBGZSLJckTIpG2fm5ShJUW3wlTjLUOooua4qpPwBZVRcTSh/AWFRCTialyXcHGlieU6+A0fwh9A2BYECxUzMVToETZ80UFkMAz+ArBsXCOA2duHFQohfIX4+ruQ4RKVhD3YjwznIQuKEb2dyIIyVXxjcfCjikleKaK3GxkM4xMBpK8IZAzR1w0Fpeq24XywDWVrFQypPVnCRQaCECgA4uA6SDMP/D5lBNzf/6auy2+qAujXJ0YDKXxIaWG5Lj5fCDPoV6bDFkjbwXEVc1TgYjouht8AIwiukewwfcq53iZpYRUAfEjbetPtw5VqvOoms8hk0spKQjweQ9oufjOAHfcTf9uDyJoPgm1704hQKMS8efOYN28etm3T3d1NZ2cnBw8exLIs72Q9Y8aMEUf2uezMhrBzc4SJCJrT6dr0+6UvJjMVZV8oZjlCOldeUkrOnj1LOBzmiiuuIBwOT+g5MunM9E7OcRyWLVtGc3PzhO6finQKUldXl5d4nUrzn2wxG+4e4jiOJ/DeuHEjBQUF4xI9AoEAc+fOZe7cubiuS3d3N+3t7Rw8eJBEIkFZWRkFBQU0Nzcze/Zsli7diLjqGpzvfQiz9Q2kT6iYEGHgColwpCJVJN3dBUqUqwaRjnINwadcJgxTEUIScWXpZPoRVgIwkP48SKjdnuO6BISrSA3RQdWdDPbhBsNqTxbIU6SHvEJEJAKBIKbrqBFeuAR/tBsnkI9l5mMMDiB9IVwzhBFJIIJ+ZH4JRl+3YiL6goh4DAyJ5YDwF+JPRFXH5viVLiw/iOjtReYXImJxpBnADZUinKiKWAmG1U7ONlQhCSavvG0LpKl0dGGBdP0IodOcHY9xKJ04juvgN4MYwlD7LHyKOm9bYEtcn6vYkS4Y0QQYYJh+DKGsprBslQdnoFw9RDLAU0p1gSHNZOETnlGwlC5WIoG0JX7Tj+sWIz7wfwlcUomU0vsupV686QukGTNmMHPmTK876OzspLW1lcOHD5OXl+cVtuLiYu97n6vObCqKWaY7rZG6Ns2QPHXqlNe1md6EY2K4UMymCd3d3Zw+fRq/389ll12W0ZXIRHdmeo9UVlbG6tWr6ezszCq1fzhOnz7NwYMHWbZs2Tnd32QNg1Ov3mKxGHV1dQghPAuscRmLIzyuPuksW7aMwcFBjh07xokTJwD13h0/flyNIz/6PzhPfwb2/rey+PMl6eACXNtNDrIEkmSEiBBJvZShdmmOqzRqpql2YZaNkHFFU5cCYgls4YLj4BcuhMKISAQZCCJilnLbiKnCR2IQ6QsgEglkME+x9HxBjMF+3GAYwiX4EjGk6UcGgrguuJYiXQjXQpgmIq8Ys7cXN78Q6QshYxEMEcBwlUkwiQTYUQiEwAS3qAQxEFU7QGmrIhwKQQiIu8rOKhiAWBwR7Qd8yHAYTOVnSDyBkFp9nLQEky5OwkXi4hMCYccglrQMMw3wh8EMI4XAcBNqROgLgAuOa+BaNq6dwDUDGJiKJSlUpIs0jKS/YtKKSj+vQ1JobZKIJ5CuxGcEcAKXwJ8/DQUl6FN2qhRFf7eklN5kRHdteXl5FBQUMH/+fCzL8k7We/fuRUpJWVkZjuNMOph3NExVZ5aNxw+FQkMuJnt7e+nq6uLs2bPE43F27Njh/SZHXQGkHNOFndkUQ0rJqVOnOHz4MBUVFSQSiYx9ziaSiaajVFJ3cpPduY12f9d1OXjwIC0tLdTU1Iyoys9WMdMFesaMGaxatepNR4/kbTO9Am5tbaWjo4PKykqKi4vPHUcuuY3ZwXnM2PEVTDeqmI6mSLLihKLjC586Vwt9zk6eUHGT4lxH/dE01Zgr4YAQWBIM28ZnGko/FbeRvjzF0jOSychK/AbSUBEnVgJhRVRhs6XqliJ9iqBiqpO+MHyYVhQzkIc0QVpRXOni2nFsfz7+vn7sQBAjGMa07WT6sqs6LMOP6B9EFuZjJKK4oTy1t0pEwJcHAwMIUyADhSgnelsZEPtD6nVHowgZQTgCaUjwhVUXK5Sbh+PauK7Al9wBeuHNUibTvaWSOkhlGOwFaromPsdG+sIgfDiui7QsbMvUvtAILAzTr16LUB2amg4LXNcgEY+DK/CLAM6sK+G2J2AU8pXuxvR3MPW/4V2baZrMmjWLWbNmIaWkv7+fzs5O2traPCMEfbIuKirKSremu75csyWz7c2Y2rX5/X66urqoqKigs7OT06dPe+bJeiQ5fNemI29yWcy2bt3Kvffey+nTp6mqquIb3/gGy5cvz/rznHfFbKQvU6qWa/369USjUU6dOpXxc6ReLY725dKatTNnzpyjWcuG6Hp4QUokEjQ0NBCPx7n88stHZXplo5hp0+XFixezYMECbxwEZPyDdhyH/fv309PTQ21tLYWFhQAjjiP35a2FhXdTdej/I9+M4veZGGbyDJrcn2H4kDhJhwtFQJAiWYwMAdJBJGwQLo4I4CQSmNgYgaCij1sOmH41YpPJjsKyFPXeiiNDQdWNBUKK6QdgxRC20oYJy1Lvhx1XZBF/PqKvF0IF4Avjj6ldm4ODFcjHl4jguIplaTgSI5FQI0CfXxkQJ/dtom8AGQyCv0CJlQkpLV5vJwgfMj9ficH1rsoMqa5P+BSzULqqOONiWxIMV+0F3aTA28AzeMZRLEYMoUayhk+FazqWsrMi6WqSsDH9AYTPxE0+juMKbNdBxm0MQ2AYYGAkM8oE8XhCSf9EAGftR+Hmv5/QdzH1+6iZhKN1bQUFBRQVFXHixAlqamq8kWRTU5N3ss6Uzq6RaybjVLElh68A+vr6vHHkgQMHhlwIFBYWMjg4CJCzYnb06FFuv/12vvKVr3DllVdy//33c+edd/LSSy9l/bnOu2I2HNFolLq6OgzD8LRclmVNWicGo7N/UgvLxo0bz9GsTbYzG14MdTRNQUEBGzduHFNakGkh1QXqxIkTnDp1irVr11JRUeGNfvSJIxPo98t1XTZs2DAibf/ccWQV7cevwvrhR8mLnsH0+/AHzCSFPkn2MJLRI1Kq4iXeNCnGVJon17FwrJg6QQbzVAQKjupeYhEQBtL0IaIxtZeKRFVR6R9EhvIQg4PIUIHyQQzkI+JRxGBEEUkciQyEEYP9ymi4oBjR3wfBEDJQiBzow/UF8JkGRqgIIz6AKxO4ph9bBvENRiAgEcKCUBHCiirrrGgCRBTy8tUoMOEgw0WADzHQi3AcpBGCvJB6rbE4AgslTBNI28CRDkjwGwZYLkJaSFsmx7Y+pN+n9n/+sCrMVgICPvVvUqikaiuO9IfQLvdSqg5ZGqYi45tBJA6OBCdhk3BsBCauayOkgTCLkNd9ATbcmtH3Rn8v4NxxpD756++63vf6fD7mzJnDnDlzhpysT548mRGdXWMqBNkwtQQTwzAoKSmhpKSExYsXE4/HPYbkiRMnuOuuu1i6dClz5syhv79/wlKJdHDgwAG++MUv8v73vx+AP//zP2fz5s1Zfx44z4uZdoOfPXs2K1asGPLFn2xnBCMLl/v7+9m1axdFRUVUVVWNWFiyJbqGN/PO5s+fz5IlS8b98WUa5aKf78yZM1x22WUUFhZOeD82EgYGBqivr6eoqIhVq1alNUYRQlBQUEDBmkpY/lus7/wpvlOv4MTBwsEwVC0yfL6kR3GSIu69bBfhuLhSYrkupi+AT0hIKGcQhEBEkh0VQo0hg8luK5CPsGxFALEcMEIqJDMYTilsykNQWAmwJDJUgoj2wcCgEjQPDuAKC9sfJJCIgZGHtCX4izDj/ZiujesP4foKMeIDOIYfI9KDnZ+PKV3lUmLmIbq7lF4ur1A52bsubqBAFThbIqIRtZ+SUqU3G8or0nbUxYfP8Ce7MR+uEVDjQ+GqY3cSYMfBDCBF0iHEFWpkaFngD6nHSzZ76oNRMS/C1qxFlUlmAqYRwAYS8SjSgUFRQP3yuyn0LaL81CnKy8uzcjIcqWtzHIempiaP4JBIJLyLr6KiIu9kPZIIWedmjReumeuuKVOrqYlgPGp+MBj0ujbbtvm3f/s3fvSjH9Hb28vcuXNZv349119/PbfeeiurV6/OyjHdeOONAF6e2ZEjR1i8eHFWHns4zrtipkXTJ06coLGxcUSvw8kWE733Gv4Yevy2cOFCFi9ePOoJfryQzPGgu6tjx45x9OjRIXln6dw3EyamDiVdt25d1gpZZ2enFzw61vs1Jvx+/J/4f7Dl/+Db+bgSNguJ60gsR40IDUNg+sAwTIRpIDGwHRvXdvGbAlPLnYQfYdlI6SJ9oTdHdb4AJCxFpIgnVLFwkidshCJJuKqjMQZ6lFjacVXnFh2EuGIhYiWgf4CEP4yZiBFwEsj8IoxIv9qPOa5y2I/HEU4MU/ggVIQvEUWGCvD39GDn5WEjMOwEIlCAIcDo6ICgH5lXoHZcjg2YSi4QFEhXKCcVW2K7CQQmPp+pfBCF7lqTdlagXpOrxoFSKnE2tgRL6cgQAZUK7jgIYSbdPFDkkiTVHoQyB5aKueg4DlbcwsRElK+m+ONbWC+EtxNNZSDOnDmTkpKSrPgcat/TkydPUlVVRTAYPKdr07cNBAIjGv7qcM2SkpIhgu3U72uu3T9S99G5fI50Xfl9Ph/vec97KCgo4Be/+AW//e1veeGFF3j++ed5+eWXs1bMUpFIJPjKV77CXXfdlfXHhvOwmNm2TUNDAz09PWzYsIHi4uJzbpOpTmz4Y6SOMIZnno13X8g80kEIwZkzZ7Asa9TXOBomOmbs6+tj165dlJaWMjAw4L3uyRay06dPc/jwYVasWMHcuXMzeowhuOX/4M5dBk//H0wnpkaNprJSchwL23aV2z0GIqlJCwQDGIZQnYVtgXCSnoIOIm6pXZShSBTSH0BElAOGxEDEY8hwCBGNIENhZdHkDyJ9PkRcBVuKaBSZX6TSnfsHcEP5OMLFF48gwkWQsBTdvrAEooOqI3Rc8AUhEVMFIjaALFRjTPJL8UX71U4qrwjpWNiuiwwVY2Jj9vUiHJDhsBqNJqJJYowPKRwcB4QhMH0+LxcMx0n+X9mG4TPADKmCJV0lA/D7FdHGVabOImErbZ5MskWSUj8wkgkHSaNgKRCui+VIEvE4hvAhlr4Xbv8mCEE+KjV4/vz52LbtCaL37NmD4zheV1ReXj6+Y8wI0L/LlpYW1q9f7+1hYWjXlkomgTcJTCUlJV5MixZs6wyyQCBAeXm5J9jOdXDmZH9v6WAyWWZz5szhox/9KB/96Edzc3DAZz/7WfLz8/nYxz6Wk8c/74pZT0+P56842g9AO4Bk2hnBm8XMsix2797N4ODgkMyz8e4LmZkF61GIYRhcccUVE/6RT6Qza21tZffu3SxatIiFCxfyyiuv0N/fTzgczviHJaXk8OHDtLS0UF1dTWlp6YQfY1Rs/CBuxUrkE7djWp0IVwV7moYaI0ohsWxLdSKA5biYJsrdw/SrE7+TUDTyQFB1OAkL6Q9DLKYCJU0VQkmoQImsAwVqnBcMqcyxcIHSTwk/mKZy9CgoxvULnEgU/D4MX/LxfEFEoADR3YVbWKa0Zo4AK6bE0HYC/HlJn8YyRdzw54MBvt5uFbuSH4SEgyMNEv58pCEwLUsFeroCgj5c4cN2XEzhw0AmLahQHaZQ3pBK9+UibBVfI9WcNhnr4irT/4RyF5HCVJ2oTIYBGMngTJn8OyEVcVRKbNvFiicwjQDG2++CG/56xI/O5/Odw0Ds6OigubnZIx7owpYOA1FKyYEDBzzS1/C99Wi7tlRCCbxJIkkVbDuO4wm2Dx06RCKRID8/H9u2iUajE9atpoPzNZhTO+bnssgCvPTSS3z7299m27ZtWU0KSMV5V8xmzpw57pc9HTbieDBNk8HBQfbt20c4HObyyy9P+03O1CxY0+EDgUB6/oajHPd4zyul5Pjx4xw9epQ1a9Ywa9YsHMehoqKCAwcO0NjYOMSxI90fmbbWikQibNiwIScLYxatQ96/Dftrt+DrOgymL7kukyRcC4FM5p+pnZlru9hWHHDBDGD6DOXonrCQhkAaQRWc6fMpM2PHQpoBRDyRHD/aasxo2WqvFokiQyGMSB9uuBCZV4yMRrAMEwNTGSTbKDspS0kEZLgomTJdAnE1IhT9g2ps6DjI/FJEZxeyIEm/R+IWliLiFkZPDzIQxucPQSKmaPLCh22CIwSGrbouwzQxDTx9mXCTUgXXASuBNIykpMEHhvPmftF2lMjcFwZDjRdVfI6T7MCM5O7QVFly0kxaiKmLBStmYfqKMT74Fai6Pq2PUAhBUVERRUVFLFq0yHOM6ejo4NSpU0ME0yMxEF3XZd++ffT19VFbW5u2gfdIu7bRBNu6sEopiUQinDhxgkgkwq9//WvC4fAQm61sFKFMBdMTQSbnw4GBgZw75h87doyPfexjPPLII6xYsSJnz3PeFTMY3wVkPDZiOtDWVPPnz2fp0qUTujLRV3sTKWY6Y00r+CcTAWMlaeMjwXVd9u7dS2dnJxs2bPCiW6SULF++nGXLltHV1UVHRwcHDhzAsizvxFJeXn5OMraGFlgHAgE2bNiQs6srAIqK4YEXsL/1Z5hHtoEDCSeB6TMJ+H1J3ZMKpvSZPtVNSOX8QdzFAoRhYkgbQyhXCyEtSCSUnmwwkhw7xhRt3U4aFLrg+sNKb+YvwujtwwmHcaTAlAamIRDROG4orDwSE3Hw5ynj45AyGnaLShWBwmdg9CY7NstFFpSo/ZvtIguLEVYCKfzIghkIKwYDgwifgfQbmJaLz4ngShNHSkTSHNkyDIQ0MUxFnzdcqY5dJndfppnMXvMhEhElzvYFVQq0Azg2wvQjpfFmJ0dy4Wir7syVElwDy7awEgl8RfMQf/Z9WLAs449zOF08dZe1Z88eSkpKvOISCoXYs2cPsViM9evXZ3TBN17XNpz6Hw6HvfDMtWvXeoLt/fv34zjOEJutTI5HH8P52JnlOv4lGo1y4403smnTJm688UYGBgYActINnpfFbDzoEZlt26OefEeDlJJjx44RiUSYN28ey5Zl9iNNl56vx3KnT5/29GpHjhzJOOl6rDFjPB6nrq4OKaU3pk0dx+r/9Ilj2bJlDAwM0NbWxunTp9m/fz/FxcWeM77+kvf29lJfX8/MmTNHTdDOOkwTPvEEXd/9WwJvfItwwI8fXzI80kQKV+3DNFXf8CsiCBLTsZGuiy1NbFxMO4owTPD5MCMx5QhiJQkTwlTEiEAQohFEIAi2gwj4sYMFyEgEM6iCPGVeWAWD9vUg80vAMJL6sUIVPZNfiqELmhTIvBKMrmRBcyxkIB/pFxg9vWpfJ2xl6Gv6IC8P6dhq9+dKbII4honPZ2BIiWFLcG1cV3WjjjQxTEOFeRpCGQvHE5CQytbLDIN0VBGznKRQOkl4wUQ6TlIInXTFlw4y+e+JRBQr4WBeVIW460eQsquaLFLDKy+99FKi0ajXtR09ehRQI8tly5ZltI8e7TnHE2xbluUVt4qKCioqKpBSMjAw4BlsHzp0iPz8fG8XOBHBdq53cpBZ9zcwMJBTwfTPfvYzDhw4wIEDB3j88ce9v9+/fz/z58/P6nP9Thaz0diI40GPyXp7eyktLR2yUJ4o0unMNJllcHDQ8z3U951MZzbSffv7+9m5cyclJSWsXr3aO76xFs9CCM9AWFObNTvt6NGjhEIh8vLy6OrqYtGiRWmnEmQLp0+f5vBF72TtDQvJ//k/IxNxpCEwDEVakIYAQyBwkvEkUjljGEGETBBwXSQmrs+Pa9kQj5Lw+THjFoZJcn9mq+7KUns0EgnwB5F9Pbh+P6Y/pMJDg2GMnh7cgmIIFSO6VdEikI/Rm8wysx1kYQlGdzdu4Qw1Yiwsw+jtQeblg7ARwsAtKFXkjsQgbqgoyX6MI31+8PuxBEhp4xcgbAGGRCSdS0xMwMGUEiwbx7KwfQbS8KHiTl3ldSlRu7WAX3VqrjIKlnYy2FSaal+GAdJNMiYlsUQC23YQa27BvOOxnH/G4XCYefPmMXv2bHbt2oXruhQVFXHkyBH27dtHWVmZNxJPZ9w4HkYaR0YiEZqbm5kxY8Y5XVt+fv4Qg23dtTU0NAAMEWyPdWE9FWPGTHdmuSxmmzdv9t7jXOO8K2bpniwnWswikYi3r7riiiu8EUKmGK8zGxwcZNeuXYRCoXP2cZNxEBmpmLW1tdHQ0MDChQtZtGjREEePiRA9QqEQF198MRdffDG2bXPgwAFaW1sxTZOTJ08yODjIzJkzmTFjRtaumkeCZrGdOXOGmpoaSkquwV1xBfLrf4oZ71B2gaahxNQueHQ8of4T0laiasMP0sVM2BjCUMXKjuNIgWMBkQHcQBB/bAARDKl9WTCEE0vg+AsIuBZgQCSCCIaQ+WWqK8vLV0WqrxuZV4TMK0N0deIWlypWZFEpRncnbkkpImGp/VhkQOWchfMUkzLgR+YFEQmlZXODAcWy7+nGJw2EYSD8PqSpTYOVBkxKkSRrmEp14FPrO0eY4EjchIWUKgXbRCBsqYTQUse4mMo5Jeka4mIgXJBSEIvHFZnxPQ/gf98DOft8hyORSLBz505CoRBr167FNE3PfLi9vZ2zZ896XZGeKmjz4clA5xI2NDRQWlrK0qVLhxBIhu/afD4fs2fPZvbs2UgpPcH26dOnh7hrlJeXnyPYfquOGacS510xgze1ZmNhIvR8Lb6eO3cuy5Yt8/zfJlvMRrt/Z2cn9fX1XHTRRSxduvScL/FkHERSi1mqHm/16tXMnj3bGyvq22YCbeXV3d3Nhg0bKCwspLe31+vY9uzZM+SKOZvsL8dx2Lt3L/39/dTW1r75Q1u4Avn327Ef3oyv9RDCn/RYFK5i4yGVryOqO8N1ENJReyQjAI6VpKQHMfU4L1SAjEVwTT8Mqv2ZiEfAFASEiwiG1Y4rWKCKWCgPmV8KsQHlmJFXgoj0IwNh3MJyjK4OZHEJxB3conKMbkX6ENEoBApxpYUxMIgM5yMGYuATyGAemCGEk8BO2EgzD38wgJQmYKuRp+uAzhMzk7ZehkqYlq5AJKL4HEs9VigP13JxpFD/T8QwEAifH0OYGEIAKupF786k65JIxEmQR+DPvoG5/l1Z+zzHQywWY+fOnZ7oXn9nPWF9QQELFy7EsiyP+t/Q0ICU0itsM2bMmPC6Ad684CwvL2f58uXexAeGkkhS7bbgzQvEwsJCiouLWbRokeeukepkn9q1TWa/ny4yGWUODg5SXl6eoyOaWpyXxSwdpAZ0jgYtuDxy5Mg54utsuIgMv3+qGfJIYu/U+062mLmuy/79+2lvbx9C9JisnsWyLBoaGrBtmw0bNnijHW2LozU77e3ttLW1cfjwYfLz870922SMXxOJBPX19Qgh2LBhw7knqPx8+LsXsL/xl5j1z2P4hfJudA2kkEkNtFChk4Ci5LmApWJYBEnXfJCBECKeQPiDGBJcn4HlOhjSxXW1AfEgwhAYpk9FvUQjyuLKH1Yeh66ddMePKkeSonKM3k5kYTLmpWAGItqrxoeRCMIXQOYXQTyu2inhVyNKTGyfD2kG8ZmGygBTRwkojZhiJzoI2wHXBlu74vvBH1bsRFcVcdN2MfxBMCSmYeA6Ehm3SUiVTGAIEMLAQFlbxWJxYsGZ5P3NTzAuXpjRZ5cJdDGZMWOGl2o+Gvx+/5CuqLe3l46ODk6ePMm+ffsoKiryLq7SsbEaGBhg586dzJkzh0svvfSc20+U+u/3+89xsu/s7OT48ePs27ePUCiEEMJjD2Z7XK8LbyY7s4ULp+4zzyV+Z4vZeMUo1Zy4traWkpKSCd1/os+vi0tbWxvr168fU381mec2DAPbtvntb3+L4zhDiB6TLWSDg4PU19eTn59PVVXVqFd5eXl5zJ8/34vr0Hu2Xbt2YRiGV9hSgzrTee66urrxbbGEgDsew3nqX+Gn/44hJELv0NQUDRBJIwsjST8XiLiDMNykE76rRNV+v9pzuRJbSnyuixEKe2bDrmXhSIGMRiAaR4bzFMnEkUpPZphKm2WGVAFKRHALyzAGepHhPIhEkKFisKJqxGjZELUhPw9pCISTwPWFsVwDnxXDjMQAxWjEn6e6MGkgDBukofRhwkCYviTxRVlUSYnSsNmOykGTIF2p/BNtgSkE+EKYrqsIJK6L5bi4TgzHdukvX0b+3z6DMQHx/mShbeNGKyZjQQuiS0pKPHawJpGcOHHCC4stLy+nrKzsnJG43i9ffPHFaTvXTIT6L4SguLjYyx+LRqMcOXKEvr4+duzYQSAQ8Lq20tLSrHRsmdplRaPR3EhspgHnZTGb7JhxJHPike6fSCQyPsbUUWEikaCurs4rLuON3SbTmcXjcfr7+6moqGDNmjVpET3SQVdXF7t372bu3LkTOrn4/f4hxq89PT20t7dz6NAh4vH4ENr/aLTm7u5uGhoauOiii9LypwRg8304c1bD/70Xw4ooU2LPh9hVLD5D5Z+ppGoQ0kbEEmoP5QtCPJ4sZOBzEhh5BTAwCOE8xMAgZl4BppVA5pUgY1GIxBQ9HoHw+zGjMUTAr1odTKX/6htUhsSRASXW7uuF/AKl/4rFkcEQRk83+EK4oTC2E8cEDDOEG/SrYu1Yit5v2QhsdOK2kCRTtYVyMbFiCDvpbmL61cjVSfFXdFH2VI5MZpGp2Buf6yCkZDARp3PRH3DmvffR+9vfUlBQMGQnlSuyj9Zbzp8/n4ULF076eVJ3vTqdoaOjgyNHjhCNRr2ReHl5OZZlec+9aNGijJ5vol1bMBikoKAAv9/P0qVLPWnC4cOHSSQS59hsZQJdUDPRmf0+ZJnBeVrM0sFo3Y1OaK6oqGDlypWjtt3ZGjOmsgjXrFmT1pcpUwJIe3s7R44cwefzsW7duoyJHsPR3NzshYGONhpNB6m066VLl3oLfO0CUVRUNIT2L4SgpaWF/fv3Z/bcl12Lc/FzyC9/AKOvTe2D7KQ9E1KNIIWKSxGoyR5mUOmy4gklTrbi+JEYYcVklIGwsrPyhRCDUaTfp9iIBcVgOpgIZCyGayWwgn7MwZhyRQ4EMFyJ8AWgp0/d3ooqjVtvHzIUgmB+8jkKcKWL0dlFwG8g80vUvs9KJONblB8iwqdcS5JNGLaFiCsHFAJhJf72qU4TqQI1Fe1eR8EYSRdhQ91fCoQwsBIWgwlJ37vv4aLb/jcXgddhd3R0eIGtemyXTcKP/n0uWbLknODZbGCksNhU/0gpJSUlJRQXF2eNlJFO16ap/6mRNak2Wx0dHTQ2NmYs2M7U+/H3JWUafoeL2Ug7s1OnTnHo0CGWLVvGvHnzxnURmeyYsa+vj8bGRhYtWsSiRYsmxMScSGeWuvubP38+LS0t3o8GMid6SClpbGykqamJqqqqEcNAM8XwBX48HvdOKseOHSMYDBIIBOjv72ft2rVD8uImhIsW4n5hO+4/3IqvaTfClzQjllJ5NSYd4w2UpRPSAtPEwkBGo/j9JkYgqBz3DT9YriJYYCDNZCfpy4O+AZUK7SQQ4TzMaAxzMI5bUAjRAUjESAT8mK7E8AUwu7sUGcRKmh7HLYhEcQvKcK0Yru1CfjGGEIi+3qSno4Hrzwe/0nsJFyDpJSmkEnxjKJsuVzE4lS9lkoLvJBmL0qd2hcJQ48mkTRVCkojF6Hd8DHzsK8x5583e2zi8w9Y7KU34KS0t9bqbTNlv7e3t7Nmzh2XLlnHRRRdl9nlPEPn5+R69vqenh7lz5yKlZO/evVnxjxyO1K5N/8a7u7tpbW1l8eLFIwq2L7nkEi655BJs2/Zstg4cOIBt25SWlnrFbSxpgiZ/TPSC9vclZRp+h4tZajFK3VeNltA8HJOhx2sxZX9/P5WVleMaE4/03OkWM+1U0traSm1tLa7rcvr0ac9DLtNuLJU1uGHDhpzTc4PBoOdorv0we3p6ME2TvXv3DhlHTthdJByGLzyL/dV78P32J2C7KlAaQ40XhYkUSZII4MTjSMdR+zEhkXFHibQTNsKxIRiESAxCYYjGVFcVUH6GQhrQ3QOFxYCJ2d2rilYiQjAaxwkX4loJHF8Yf0cXdkEhAhNTAKEQRkc7tj+AmZ+nHDwAwoW4hh/hOkr3FrNItpWqyRQSMFSWmUAtBxMWwjDU3k8aihCCLxncKRQbUiYLoQTpCqyERXegBPvT/8WclWtHfTtT04u1sLm9vd0b3YXDYa9rS7d7OHv2LPv27WP16tUT/r1MFloXtnz5cq+IjuQfWVBQ4H0Hs5FgbRgGvb29nj+qHoOOlrCdum/W55jOzk7Onj3rpRJo9mZRUdGQ9z0T8oeWP1woZjlEOl8ivTPTrheu66a1r9JIhw05EmzbZu/evQwODjJ79uyMfpjpdoWa3aeNl0OhkLewfe2110Yc26WDeDxOfX09hmGMzBrMIXQhsyyLt73tbQSDQfr6+mhvb+fEiRPs27ePkpIS73VNaIdw1/+H/dRyfD/5sgrbFMr2SQLCVDujhJtAYhDw+TAsVxUHXwDiMfUYgTDEEsooOBJFBoMYfb2KhZiwVHcWNBCdPbjFpZBXgOjpwS0sRvgMfP29ShSNg5tXiK+vHycQIm76MGwLGSrAJ13Mnh6VIJ0XQiScZPyKC/iQmDpaDKEZmU5MiaF9fpVt5lOkE2z1ulTkS/J9UO7BaqxoCKTjkohbtMxYTPjvfsTMiooJfWbDu4euri6vy3Jdd0h3M9J3qbm5mUOHDrFu3bopp4G3t7eze/duVq5cOSRmaTz/yFSnnBkzZmRk39bT00NdXR2LFy/2RqojjSN18Ohogu0FCxZgWZYn2N6zZw9SyiE2W5lS/3+fipkYHBxMK+lxKhkvtm2Pe7I/evQo3d3d9Pf3U1ZWxurVqyf0YWpa+ZVXXpn2fTSxxDRNioqKcF2XVatWpX1/jcHBQX71q1/xnve8Z9TbpKZPr127dgglX/sztre3097eTmdnJ8Fg0CsAY10t9/f3U1dXR1lZ2Zg7xVxAv39aHDvSHia1C+jq6iIvL897XWmTEnZtx/zqX2EkBlWDYyrjRcuOg3Dx+4OKxo+JwEbajlIfC0USkb6AYjT6TMUQNE21z/L5EIO9yIIiwIBYVMXHAEQGkPn54DgYgwO4hSWqEEkgHkNaFlY4jJFcbQmfgSkdjLiNIR1kKAymL8nAt1XH6JqKXKIDR119Z6my2xwbaZhKM+cLKocPmexE3eTu0HaJJhxOL3k7M/7mG5NyvRkO3d3oz6u/v/8civypU6c4duwY69aty+oYOx20trayd+/eCXeDqWPWjo4OBgcHh/hHpnPhqAvZkiVLmDdvXlrPmappSyXA6a5N/1ZTu8rOzk4vCcO2bS+vMJ3fiZSS2bNn85vf/CYn+WWpmAoHkN/ZYtbQ0EBLSwvLli3LyGaps7OTvXv3cvXVV6d1++7uburq6pg1axYrVqzg+PHjDA4Osnbt6OOa0RCNRtm+fTvXXnvtiMfd0dFBfX098+bN49JLLwXeXPDqJXIqHMehs7PTK27AiMt7fTW9cOHCKbem6uvro66ujoqKCk+4Ph50RpY+WQ4nJYx58XK2CfG5W/F1n0UaLgnHVrIs00QIiUCosaMQSEPtoYQhkT6/F6EibEUekaaRtM1StxWDfci8fDX9k6iRoHSVx2MwjASMgb6khZXAdpL5a5F+5R5iBpBOHFcIHFT+mi9J1jANSNIXk6NGUPu7pAzAsgEnKQewIBl9I6UDmEpjl3RFcaUgZksOX/EnLPiLB3P+G9Z7UX2SBXXCXLJkCRdffHHORcOp0MSiSe1jk0j1j+zq6vJSL7Qgevjr0ueKSy+9NK1CNhzDSSTDC5s+B+jfUCKR4Pjx47S2tgIMIZmMlEqgYds2ZWVlHDt2LOdas7dsMXMcZ1TavXanaGpqIi8vj7e97W0ZPYe+cnrnO9857m2bmpo4cODAEGLJ8ePH6enpoaqqasLPnUgkePnll3n3u999zg9Bk1hWrlzJ3Llzhzh6jFTIhkMLSrWoORaLeVqWjo6OadlZ6CK6aNEi5s+fn1ER1VfLumDHYjHKysq8HceIy/FEAut/34I4vAN/wMQf8KXkUArlfI+jaOumX+2mbEvFzkhHdUEBP8Riao8Wi0IwpNiLlpUM0Iwjg0HVhdmO6pYCQaQwEZF+pWP2+zGNAPhNRDSiImnyC1TXFbeQAlwMdVtACB+mIRGYGE5cETwMHwQCgA9hx9WfMVTdc0gWZAmGgXRcpC3p94U4cNOnWfW+P8kKuSFdaHPtM2fOUF5eTm9vL/F4POs+i6Mhdaw5Y8aMrD624zhe6kRHRweJRGII9V+nSyxdunRSzOBUDKf+p54PdHFrbW2lpaWFyspKT7Dd2dlJJBKhqKjIGwWndpW9vb3MmzeP9vb2nI1/9+7dy+23305jYyMf+chH+Id/+IecXUSflzuz0aB3SIlEgiVLlnhXIpkgHTssXTjPnDlDdXX1kB/GZC2p9OOnalUOHjzI2bNnWb9+vZd+O1H9WKqg9NJLL6W/v5/9+/fT1dXl2V9FIpEJ79kyxalTp2hsbGTVqlWTKqKppIRU2n9LSwsHDx6ksLDQG0dqB4jO/n52v/c+1hV+j4q9L4MjkLiqkLkSMHG1c7ztInBxzRCGlVDUdn8QbBsZyleRLaECjME+ZDisyCBCIv0hjJ4+3KLCZIcmlZbN5yduBvG5Nv6BKLIoCNE4+IO4gXxEPIqwbKThQwR9GFJi2i7SsdWoSbjYGAifieEPYLgkc8cMJD5lrOwkkEZAFWc32WXGXVygJzyTg3/6BSqvvia3cT3DkBqqedlll5GXl+cRDTo6Oob4LOoLkWxq2k6fPs2RI0eorKzMyVjTNM0hJA39ulpbWzl48CCgzIfz8/OnlPqfSCS826QKtnUYcGdnJydOnMDv9zNjxgxOnDjhdWO5In/F43E2bdrEtddey+OPP87999/Pf/7nf3Lbbbfl5Pl+Z4qZHlMVFRVRXV1NV1dXVhw8RkurtiyL+vp64vE4l19++Tmd6WTNgkFd5fn9/iHPtXHjRsLhcNasqQ4fPozrurztbW/DNE2vs9H0+HT2bJlgeCL1cAeWyUJTrhcsWOAt7zWJxO/3k5eXR3d3N8uXL6fsnd/G/snjmP/5BQxDIBzl44jrJJ1CBMLwI6WFYaugS6RAxKxk/lkUGQgg4hZuuAhhWWrH1j+ACOfhFhRjdHYii4vBDOAkEjAQwxfwYwTCyv6qpx+ZnweRBMJQRsDSF1a+i7aTHFmaCJ9ASAMDMJNOHo6jHDsMV0W5GK6D4QuC8Kt9n0ovRSJxXWidtZxTH/081dXVUzra01l62ldTd1+pMg1NZhhN0zbWWGw8nDhxguPHj+fk+zYSUl+X9i/V0xTtHzkeOWaiGEmwPTAwQFNTE7Nnzz6HRBIIBDwWseM49Pb20trayqc//WmampooKyvjscce48Ybb/RWGtnC888/T29vL1/+8pcB+D//5//wqU996q1VzIafvFtaWti7d+8QPVc2dGLAiMVMky/y8/PZuHHjiESFyVpSCSFwXdfzp8vLy2Pjxo1Zc/SIRCLU19cTDoepra31XkPqF1vvozQ7KlsiWU37HxgYyF0idQpSwx8dx+HAgQOcPXsWn8/H4cOH6ezsZOb6aymfs4jQI/dgRnsQhhIQ644MEqqz8SVNiW0baQYRkYjao8UsQCqz4kAALAnhYoy+bgiFcYtnYPR04uTlYyPw+fyY8YSaaZoGsrAYGY1jODZuOA/RHwEcZYLs96sCaqCiWSQeTV9IMPx+pC+AjMdxHBfbFUg7gcDAMEwMVclwpcGR5W9n8EP3U5li2jsVcByH3bt3E4/Hqa2tHfPEPZ6mTbNZJ6JpO3bsGKdOnaK6upriKbTlgjep/ytWrGDu3LkAnqt+e3s7p06dYv/+/R45pry8PG2SxniIx+M0NDRQUVHB4sWLh5gij0T916YGu3fvZuvWrfyv//W/+NnPfsZnPvMZ5s2bx0MPPZS1YtPQ0MDGjRvJy8sjEomwZs0ar3vNBc7LYqaho0BOnTrFunXrqEihFGermA0P+Gxvb6ehoYFLLrlkTFunyYwZQX25urq6OHTokOeuD0OV/Jl+2Xt6eqivr2fOnDmjpmibpjkkhHAkV/yKiorR91GjYDjtfypHXK7rcvjwYbq6urjssssoKCjw2HanTp1i/4BF8W1fZPX3/p6CnnZMH57dFbgqJsVxwTDftJ/yBZMWWQJpGoiEtppKgGHhFpSpeBc7gl1QhujrwRcMYoSCSCOAiPQpe6xYBBnKR/r9iEQyWiagUqBF3ELYcbUw85nKFNk0wVQp1iKRUIQUI4ApBKa0kZg4rsRJOFiuQ8IIcfCdf4J4962smeJCZts29fX1uK5LTU3NhD7zkTRtustO1bSVl5dTWlp6zuuSUnL06FGampqoqanJKlszHXR0dLB7925WrFhxDvW/uLiY4uJilixZMoQck45/ZDrQiQM6aHd45ExqYRuJ+j9jxgzC4TDPP/88kUiEl19+edJkmVT09fUNIZboJqS7u3tM79pMcd4WM61HGh5sqeHz+dKOgBkJqW06DI1TWbVqlXeFNdb9J1NMQaWtrly50uuUJkL0GA2axbV06dK0mVTD92yj7aMqKirG3LMNDAxQV1dHSUnJkDiPqYDuDKLRKLW1tZ7eUGuJUsNHD/6vx7jo0U9RevYwfp8fnw9MDMValC4iOfZz/SHljo+DNPyKrm8GEa6F9OdhxAch0Q95+bhxC9k3gMgvxowMIF0Q/iAynIyJCechenpVFxYKgWEgbEt5LxomBPJUYcNVQZqODQZIYYBrqh2ZbSF8fhABkBIfyo8yVljAzvfehViyhnhXF6+++qrX2YzL+pwkLMvy5CrV1dWTtr3SYZ3z5s3zNG0dHR1DHDtSxfWHDx/29sxTrZcarZCNhFTTgJH8IyfqsBKLxdixYwdlZWVefE0qRhpHDhdsHzp0iFhM6Svz8/PZtGlTJm/DqPD5fOcQj4LBoPd6s43zsphFIhFef/118vPzzwm21Bhv5zUe9NWJlgFoh/0NGzakNabIdGemSSWO47BixQqvkLmuO4RuO1FIKb1Ry2TFqcP3UXrPdvz48VH3bF1dXTQ0NDBv3ry0ncizBW30bJomtbW1o3YGQ8JHv/0ysS99CuOVJ3GTxArDMPAZAtPnR0pHWVAJkMKHiEeRwTBioA8ZLkBEI7jhAuV8H4ng4MMMhDGicWSoEKKDYMcRpg8ZKkQk4koLJgyMri6k6YdgQI01MUlyLJNu9yhmolAekTgkPRZNsCRSuKrI2ZLBWQv55S33smRtFZdccskQs+fDhw/nlEUYj8fZtWsX4XA4bV/SicDn8w2ZHugu+/Tp0+zfvx+/3+9pPac6YFKLsVetWsXs2bMndN/h/pGRSGRC3Wg8Hmfnzp2UlpaOG52T+pypJJLGxka++MUv5lRfVlZWxt69e4f83cDAQM6mNedlMfP7/Vx88cVjOmqnXnFk+iMyTZNYLMaePXsARnXYH+2+Ex0z6qywaDRKKBQiPz8/K/sxXYx7e3upra3N6hXq8AVyV1cXbW1tQ/ZspmnS3NzsFeephE4QLyoqYvXq1WlfDPh8Pgoe/P9gzWX4/uOzyERMRaPYNnbCVtmXPj+ma4PrIP15ygHEl6fGhIYP0duLFQ4jXZVCbDg2GH4VFxNQidIgMXr7kPmFylrLtZF5xco30U4gooPKnkpZ54PpV7R7w0RYMcBBCr+6jUwSV2xV+HpXXMbr1/05K1ev9jqD4WbPOntOswi1M/5ks+ei0aj3vk9FFz7csWPPnj10dXVRXFzM3r17vbHdRKOHMoEuZNmSueTl5Z3jsNLR0cG+ffuwbXsIiQRgx44dFBcXs3Llyow+v1OnTnHTTTfxgQ98gK985Ss5u/Csra3lW9/6lvfnkydPehdXucB5WcwCgcC48Qx6nGHbdsZfXCEEDQ0NzJw5c+wMrREw0c5Mn3RDoRAbN27kjTfewLKsSRcyvQAGuOyyy3JqTTWcltzT08ORI0fo7e31tC6u6+ZcR6TR29tLXV3dhGNrhmDTh7EXLMf83Mfx9XWoTsqxkI6LaydwhEQYBkYsjmH6EIYy8pWGwDElImbh9/uRcUt1bomo6vIiMdxgSBFJgvmIri7Iy0MG8xB2AkU/9EHArz2AFSwHQUKxHaVf2VTZSacPKZBSIE0f7X/wh9RVv5u1a9aMuucQQgzpskfKnktbhJ6CkRKapwqu67Jv3z76+/vZuHEjoVDIG9ulRg+lar+ymYSuL+TWrFkzZIefLQzvRgcGBrzkif3792MYBnl5eRlr2Jqamrjhhht473vfy1e+8pWcXoS8/e1vp7e3l+9+97vceuut/Ou//ivvfOc7c3ahcV6KpkGdpMeClJIXXniBq666KqNja2lpoaGhgYsvvphVq1ZN+Ac5notHKrq6uryTriZk1NXV0dnZyYwZMzyixUQLUeqOauXKlVNOw96/fz/d3d1UVVUhhPDGkb29vSPqvrIJzcLMWpRIZyfmfbditJxEuBbCMJGuo7RnrotjmmDHMaSN9AUx4jHcUBCfEAjDp9KfI1FkcQkiEVNi5ngcmV+kzIsRauwYiSF9JjKvQNlkOcqlX0ipwkSlC66jNG6JOML040qU16IhcAMhTn7wXg7PWUplZWXGu4fUcWR7ezvxeJzS0lLvMxvtYkSHas6dOzf97LkswXVd9uzZQyQSobq6ekQhuJTS60Y7Ojro6ekhPz/fK9qT0bRpe6xcFbKxkEgk+O1vf4vf7ycUCtHZ2Tlh/8iWlhauvfZa3v72t/Mf//EfU3K+eOqpp/jQhz5EQUEBruvy05/+lJUrV+bkuX5nixnAiy++yGWXXTYhBlMqQ9Lv97N8+fKMRgVjuXikYrh7SCq7SAsu29raGBgYoKSkhIqKCmbOnDnu1WRHRwd79uzhkksumVD8TDagx6W2bVNVVXXOSUXrvtra2ibkG5kumpqaOHz48KSF2OfAcRB/czu+nb9AmEKJogHhugjpInFwMCARwfEH8cWjuKE8fIkIhAsQUiL6enHLZiCsuEqFHuzDLZmBsGxAql2Z6yZHkA5gIA1TFU+fT8kFYnGkz6eSpRHKKcQFp3AGh/7qCzT7w1RXV2eVuadJP/piZKRxpA7VXLBgwZTboaVS/6urq9O+8LMsy5OgaIutTAyEdSHLhj3WRJFIJNi5cyf5+fneKH0k/8ji4uIhkobUz6e1tZXrr7+e2tpannjiiSm98G1ubuZXv/oVl112WU7fu/O2mCUSiXHTprdt2zahq1Pbttm9ezcDAwNUV1ezb98+5s2bNy5zcbTHevHFF/mDP/iDEX9YUkoOHTpEc3Oz50aQylgcfkLXBrvt7e10d3d7cRQVFRXndDanT5/m8OHD5ziBTwW0WbBe+o/HXtN7Nv3a9BgyEz2bpmGfPn16Ul3JuHj0c/i3PIEwpGI3Jq0SXdvCsS2EP4APVGK1beEC5mA/TkEhBuAb6EeWlHo0f9HThSwsAMOnCEsIpPZ6RCSd8R21mwuGFZMStSPTQZ3WwhXs+avP0xOLUV1dndPfY+o4srOzE8MwKCwspLu7m8WLF7NgwYKcPfdIcByH+vp6HMehqqoqYwKB67qe9mu4gbBOaBipQOv4muksZHl5eV6y/EgYyT/y5MmT+P1+Nm7cyB/+4R+yatUqvv/972ctaHUimApvxvNyZ5YuJkKP1zurYDDIxo0bCQQCk6LX6yubke5v2zYNDQ2erCAvL29cokdqzIY+mbS1tXlfSD2KbGtro7W1lZqamilxOUhFb28v9fX1zJo16xxdy2gYvmcbSc823mgLho41c56/dvffYS1di//hzyCsqPLDcx1sx8UIhPC5UlHok+ND0zCRBaX4Bgewg2FioQJCnd1YhcUYjoUomYkY7EMkBiCvIOn9KJCuEmxLYSriiFSJ0NK21e5OCqSExNuupeEP7yAai1FbW5tzn8XhouYTJ05w7Ngx/H4/R48epaurK63PLBuwbZu6ujqASVP/DcMYIkFJ1bQdPXrUmyCksghbWlo4cODAtMTXWJblGSqMVchgqKTBcRy6u7v5xS9+wXe+8x06OzspKyvjyiuvpLm5mfnz50/hq5g6/E53Zq+99hqLFy8ed9TU2dlJfX09c+fOHeLYXldXR2lpacZXmi+88AJve9vbhpxYU4tmZWWll5uWKdFDdzatra2cPXsWKSUzZ85k7ty5OdcQpaKtrY29e/d62UzZGDENH22NtmfTFweWZY041swZ9jdg/s3HoLMVJ2HjNw1Mn5GMhrHUKDEQgtgA+MPg94FlI00TV4Cvt4d4QQGGm+zQTD+mY6n9mhRqr2b4ku4fvqQ42g8IpBBIw0/0T+6ibt0VSCkn1ZVkiuGhmvozS91H6c8sG4GWqUjVsFVWVub0u64dcXR3Y9s2+fn59Pf3s2rVqimfgFiWxc6dO724pExG8z09Pdx4443MmDGDa665hp/97Gf88pe/ZP369bz22mtTOiZ+y7rmAx7Tbyy88cYb444JtQv98uXLzxER7969m/z8fBYvXpzRMb700kvU1tZSVFQEvBn9MHv2bK9zycQseDii0Sj19fX4/X4WLFjg0eM1a0vv2XLFZNRmwatXr87Z4jvVX7Gjo8O7Si4uLubYsWNjZqDlEqf37aXgvo8wo7cdvwCBBNcFJDJZvAj4EbFBFfLpWOr/UqoOrKcLJ18tv5EurlCFyzBNTFyE66oCGAwpar6r6PdOuJDo33yJXfmlBAIB1q1bN6V7DnhzN7l27doRu5KRxpGZsCNHQiKR8C4K165dO6WvXWs2jx8/TjgcJhqN5sSKajTojkx/7pkUsr6+PjZv3kxxcTFbt271Ouje3l727t2bcdpIprhQzMYpZjt27KCiomJENpvruhw4cIDW1tZRHbT37duH3+/3rKQmitSdnabOLl261BOv6uOfjKOHHu0NzwHTBBId9dLf3+8tgCsqKrLyeem9n34Pp8rzTnejZ86coa2tDSEEs2bNoqKiYtK+keki1Sapcu1ayv7xAcxXX1RbLtNQKc+g7KfiCQj6VZCnz0QM9iPz8hCWowyKoxGEFcPNV++fTMRxJbhCgOnHcCX4fBhCmR67sy5i4F8fZ1dr55TpuIbj5MmTHDt2LO3dZCo7sqOjw4seymQcqcXY6YzXcgEdIaPPG8Nz2nKpabNtm127duH3+zMuZAMDA9xyyy0EAgGeeeaZKT93j4QLxWycYlZfX09xcfE5wXI6KsayLKqrq0dlBh48eBApJStWrMjoGH/xi1+wcuVKurq6OHXqFJWVlV6E+WhEj4mgtbWVffv2pTXai8Vi3siuq6tr0uOfVHuoqqqqrGp10kGqo0h5ebn32iKRSNp7tkyh43g6OzupqqryROji0X/E/4NvqyBPKVWUTCKm76RYh4ah/Bf7e5B5hRhWAhnKQ0oXEdf6MsCnUqUdw4C4hW2YuK4ksngFXV/6Jsebmye0m8wWdFdy+vRpqqqqMr6AyXQcGYvFvIT1iYjgs4XhhWw4Uq2ohksaJqtp04XM5/Nl3IlHIhFuvfVWXNflueeem3KLr9Hwli5m6aRN79mzh3A4zJIlS7y/0zqYoqKicdl2R44cIR6PZ2zp8uqrr+Lz+byimS1HD+0Tefz4cdaMIYodDZqO3NbWRkdHhyfEnDlz5oj2OMMRj8epq6vzflTTtadZtmzZOeLQdPdsmcJxnCFapnOK5QtP4//8XytzYSmV+bDrKg9Hnw+iERAGMr8AMdADgTxIxMAfAJ+i32O7Kn8skcANBtFJ0v1Xv4cjt93J2bNnvbTgMcNHswwd23P27FlqamqydiJMjXzp6OgYdRwZjUY9m6ZM3S0mAz1WraqqSqsbzaamTRNdDMPIeD8Yi8X4wAc+wODgID/96U+99cf5gAvFbJxitn//fkzTZNmyZYAiKTQ0NLBw4cK0/AGPHTtGf38/69atm/DxRaNRXn31VfLy8jx3+FRX6kx/iJq119XVRVVV1aS1RK7retT4trY2XNelvLx81JGdFmLrE8p0jLeOHj2aVhEfvmcLBAJe0c5Ez6Zz5QAqKytHL+JHD+O748MYbS0IqZyppGkqAkfAj4hFwXGQBYWISLK4mYbyZ5RSueKHgklHDwn+EIm7/5rO926moaGBxYsXD+lGp0KEnhqqWVNTk7Pfux5H6s9NjyOLi4tpbm5m5syZU+4qAm+GeqZbyEaCvojURRvS07Q5juM5smRayOLxOB/+8Idpb2/n5z//+ZQzncfDhWI2TjE7dOgQtm2zcuVKjh07xrFjx1izZk3axp8nT56ks7OT6urqCR1bT08Pu3btQgjBkiVLPCfsyXZkiUSChoYGXNelsrIy66w9nbHU1tY2ZGSnC8DAwAC7d++eFiF2aleQyX5uJD3bWEV7OPR4S+9pxj2hRCKYH7kF3+EDSad9WxWygX5kYSEinkDEo7iFxWokaVnKW9E0lb7MZ4ILbkkp1j//O62LLmXv3r0jagdTi3ZnZyd+v98rbOl02uNBh2pq/eVUdIEag4ODNDc3c+rUKaSUnr4yF+zI0XD69GkaGxupqqrKWhFIlaGMpWlzHMeTHlRVVWVUyBKJBLfddhunT5/mxRdfZMaMGVl5DdnEhWI2TjE7evQo/f39gCow1dXVE2qtm5qaaGlpoba2Nu37nDlzhn379nHppZfS3t7OzJkzPXPdyXRkg4OD1NXVUVhYyOrVq6eEvZVKIOnt7QWgoqKCJUuWTKkLeWqYZ1VV1aS/a6MV7dH2bDqMVXsNpl0cXBfj/rvwvfQcwpWIRFy5ecRikJ8Hto2IDCBDeZAXRrqKCSkcB2n6cS6eh/1/n6QpmQieTjeqNUS6aNu27V39Z2KJlqmzRraQao81f/78IZ1N6jgy08yv8XDq1CmOHj2a1UI2ElI1bd3d3QSDQWbMmEFvby+GYVBTU5PRb962bT72sY9x6NChrOeRZRNv6WLmOM64eWVHjhzh5MmTFBQUZKQ/amlp4eTJk2zcuHHc20opaWxs5OTJk56Asq6uDtu2mT9/PmVlZRlfIWuyw8UXXzzlfneatXfq1CkuvvhiBgcH6erqIhwOeyf/yfjZjQc92pNSUllZmZOTqd5r6KJdUFDgdaM6WHIy0TXiG4/i//evKBG1VNZXOI5nQ4VtqRGkoXZp0jBxqjdgf+f7nGhq4sSJExk5mqTGorS3tzMwMOAxWmfOnDnuBYl+7fq9n+rdaF9fH7t27eKSSy45JyFjtHFkNogWGpqxOdXp1I7j0NHRwaFDh0gkEl4kjL4gSfc85jgOn/jEJ6ivr+fll1+ecBTNVOJCMRujmPX09LBjxw5M0+Tqq6/OqJC0tbVx5MiRcTUX+uq1r6+Pmpoa8vPzPWucpqYm2tvbvTgUPdZK9yqrqanJ08FNdXyKdiDv6ekZwtqzbdvzs2tvb8cwDI/yP5miPRzaGivt0V4WMHzP5roupaWlLFq0aHK+kS+/SOCBexB9fSp4Mx5XY0etSQOE8OH6/Tjv/wD2577ojVWz5bM4nNGaekFSUlIypFhoLZPP58u5IHkk9PT0UFdXx8KFC9MyLdA+pu3t7VkRa2uC1VQXMlDnk1Rv01Qrqr6+PgoLC72OdDRNm+M43H333bz22mts27Ztys8dE8WFYjZKMdOaLu1IcPnll2f0HJ2dnezbt4+3v/3to95G71JM0/QcGIYzFnUcir76j8fjXmHTibjDoQ2Pz5w5w9q1a3OW8TMadEc03n4uNV6jvb0dy7K8H9pory0d9PX1UVdXNy30c1DfoYMHD3r2Yal7Nv3aJjzWOnkS/4f/CLPpNNJnIvr7IByGQAApQfoDJB76e9wPfJj9+/d7o/Fc/LZ0Lpb+3ADvtRUUFLB7927C4XDG7hKTgTYXyDTxYCx2ZDrjSF3Iampqppzx57qu52Yzkj1XPB4fYoysNW3l5eXea3Ndl3vvvZeXX36ZV155JTupETnGW7qYua6LZVlD/i7VvHfdunW4rptWZzUauru7qa+v553vfOeI/65dwsvLy1m1apV3XGMRPXQGkd7XDAwMUFpa6o21QqGQR/8eHByksrJyylNyI5EIdXV15OfnT6gj0mMt/doGBwfPeW3pQMfNL1q0iPnz50/5WPX48ePeuFhfROg9m74gyVjPFoth/smH8f/216obi0ZBSOSci4n/x3/gVNeyZ88eT783VZR7TUZobW0lGo0SDAZZsGABFRUVU0r46OzspKGhgaVLl2acyZWKiY4j9Wc/0f16NqALWSKRoLq6etwLweGatvvuu4/8/HzKyspoaGjg1VdfHTf38XzBhWKWUsxSU5q1piudzmos9Pf388Ybb/Cud73rnH9raWlh7969LFmyxDPm1ISUiRA9otEobW1tQ/Y18XicUCiU1hc62+jp6aG+vp45c+Z42WqZYvguStPHKyoqzomg0Dhz5gwHDhyYFsf/VEeT8UZ7+rXpsdZYKQYjwfzM3+D/r++D4+AuXkziR1uwSko8tup0+CzqUM3i4mKKioo8bVQqgzCXVk06oXnFihUZJVWkg7HGkR0dHZw+fZqampqsxuekA9d12b17N7FYjJqamgl/9lJK6uvr+ed//mdee+01ent7Wb58OTfccAPve9/7uOyyy3J05NnBhWKWLGb6R5iXl8fatWu9L4KmyP/BH/xBRs8xODjIL3/5S6699lrv7zQh4vjx46xbt46ZM2dmzdGjs7OT3bt3Y5omiUSCvLw8r6uZChqydhTJWqBlCkbKMEvVfAEjdkRTBU0/7+/vH9MVZiRkSo0XW7bg/+//JvFf/0UiqSWaLp/F0UI1h/srmqaZE6smndC8atWqKSMqpGaZaY2lNunOFTtyJOhQ0Wg0mlEhA3Ve+tznPsd3v/tdtm3bxuzZs3nhhRd49tlnyc/P52tf+1oOjjx7eEsXMymldxLRbLPhncTAwACvv/467373uzN6jlgsxiuvvMJ73vMeDMPwxn89PT2eA4LrujiOMyn9GLzpOq8X3prRNNylo6KiIisBlqmQUnrMrVyaBWtoB/LUfY3f7/fGK1O9cNddvc7DmgxjcjQ921h7tmg06rnSTIfPoiZbLFiw4Bzrt1QM348mEgnPhWQyRtYtLS3s379/WhKatT3XqVOnWLp0qSdHiUaj3hg5W+zIkaAvogYHB6mpqcnoPZRS8k//9E984xvf4OWXX87YsWg68ZYuZnofduTIEVauXDkiWycajbJ9+3auvfbajAqNZVm89NJLXHPNNZ54UQjhnfCyZU2lC8loycjapUPvojJlRo4E13U5dOgQbW1tVFVVTfmeQPtkRiIRDMMYQiCZOXNmzkdt2rRWu69n82o8nT2b1rBpo+ipJrroHdWll156TmrEWNC7X8367Ovro6ioaAjtP53XcubMGQ4ePDiq834uoacszc3N59hzjTaOLC8vz5oUJVuF7Mtf/jKPPPIIL730EpWVlZM+runAW7qY9ff389prr1FZWTmqmDGRSPDyyy/zrne9K6OTlOu6vPDCC9TU1LBv3z7Kysq8q55sOHpow9r29va0XS30sl7v2TQzMpOTv23bQ8gGU20WHI/Hqa+vxzRN1q1bh8/nO4ccU1JS4o0js318ejw9VdZcw/ds4XCYWCzGnDlzJibGzhLa29vZs2cPy5cvn/SOKh6PD6H964iesazDtEXUaKa9uYTWhZ45c4b169ePSbJKHUemsiO1DVUm5xYppTfWXr9+fcaF7NFHH+VLX/oSP/vZzyZk7nC+4S1dzEB1XmOdAHQxeuc735mx9dNPf/pTTNMcEgefCdFjOCzLYvfu3SQSiYxZa+kwI0dDLBbzMtBS94xTBe1oUlxcPOpoLRqNeifI7u7uCZMsxkJvby91dXXMnTuXSy+9dMo7otbWVvbs2UN+fj7RaDTrFlTjQY/2dKhmNjHWqFV7EOppRK6dNUbCRArZcLiu6zE/Mx1HSinZt2+fp0vN5NwkpeSb3/wmn/3sZ3n++eczlh+dL3jLF7N4PD7mv0speeGFF7jqqqsmfHx6ln7kyBGWL1/O/PnzhxA9JlPINPVdi4GzNdoazowsLCz09mypP9j+/n7q6uqYMWMGK1asmJYdTX19PRdddFHajiaaiKAJJH6/P2PTYE39X7x48bRExLe2tg7xWdQWVPqiZKSTfzYxXqhmNpE6atVyjVAoRDwen7Yd2ZEjRzzn/8nKXiY6jtSFrLe3l/Xr12dcyJ544gk+85nP8Oyzz3LVVVdN6jWMhs7OTtavX8+2bdu8C/m9e/dy++2309jYyJ//+Z/zpS99Ka3f7/bt27njjjtob2/nwQcf5FOf+tSQf3/LF7NEIuEVl9Hw4osvctlll02Iaqu9ALu7u3Ecx6NpT3asCEq71tDQkBXq+1hIJBLeribV7SEYDNLY2Ogt+6e6I9FEl4nuaFIx/Mp/IjtE3ZFMB/Uf3iwko/ksjnTyz0SrNxq0IDgTe6zJIlUHWlhYSF9fX052UWM9/+HDh2ltbWX9+vVZP2eNN440TdMTw9fU1GQ8jfne977H/fffz09+8pNRNbCTRUdHB5s2beLXv/41x48fZ8GCBcTjcZYvX861117LAw88wD333MOtt97K7bffPuZjtbe3s2TJEu677z4++MEP8sd//Mc8/PDDQ479QjFLo5ilpj2nA53VJaWkurqaN954g+XLl3tX/5P5sWkN1Ug5XLmEtp86ceIEfX19+Hw+5syZM2UjLQ29I8kmY3KkHeJoDLsTJ05w7Ngx1q1bN+XO4TqDbqI+i5PVs6U+v07Gng5BsO6IWlpaPLLFaCf/4Tlm2Xr+Q4cO0d7entMIG43UcWRHRweRSIRAIOA56mQyWpVS8j//8z/cfffdPPnkk0MkQ9nGu971LjZt2sS9997rFbOnnnqKj33sYzQ1NZGXl0dDQwN33nknv/zlL8d8rEceeYTHHnuMAwcOIIRg69at/PCHP+R73/ued5sLxSyNYvbqq6+yYsWKtMYp/f39Xvjf6tWrEUKwY8cOYrEYs2fPznhXo08kp0+fZu3atdNyIm1sbKSpqYk1a9YADBlp6ZNjtk8gw5+/ubk54x9yus+T6vTf39/vGevqv59MOvJkjisbPovaVmuierbUjqS6unrK04V1IWlraxt1tKedOvTri8fjQ5ifk4k7Si1k69evn3KikyZ7dHZ2kpeXl3FHumXLFj7xiU/wP//zP9xwww05PeZjx455MU+6mH32s5/ljTfe4LnnnvNe14wZM+jq6hrzsW6//XbC4bCndWtpaeGaa65h//793m2mophNjWowQ2jfw7Fgmua4UTHwZnDnokWLPK2N4zisWbPGS2U+ceKEJ/atqKhI60voOI637K2trZ3yE0nq82/YsME7kZSXlw/pag4fPux1NXqklY1djTYr7u3tpba2NqfWXEIICgoKKCgoYOHChcRiMe9zi8fj5OXl0d7ejhAip04WqdBhqj09PdTW1k7qos/v9zN37lzmzp07JOpl3759OI7jfXapezYpJfv376e7uzsno7XxoEM9u7q6qK2tHbWQGIZBWVkZZWVlQ/ReLS0tHDx4MOPwUSklBw8epKOjY9oK2aFDh+jp6eGyyy4jHA4P6Ui13EcXttHYkc888wyf+MQn+P73v5/zQgaMaIPV19c3RIcohMA0Tbq7u8ecNPT19bFy5Urvz0VFRTQ3N2f3gNPAeV3M0sF4xUyPfxobG1mzZg2zZs3yaPegTiBz5szxFvW6sNXV1WGa5phCZk09NwyDDRs2THkWlA7zlFKO+PxCCEpKSigpKeHSSy9lcHCQtrY2Tp06xf79+z0Pu0z9+VLFyLW1tVkPEx0PPp/PS5iuqanxfCN37NjhidBzOWrVIvtoNMr69euz6nGonTh0xpresx0/fpy9e/dSWlpKeXk5XV1dOXn+dKALuSY7pPv8wy9KUh1WTpw4MaGOVBfS6SxkwztCv9/P7NmzmT179pBx5NGjR9mzZw9lZWXejn7ZsmX89Kc/5fbbb+eJJ55g8+bNU/oaUuHz+c75DYdCISKRyJjFbPj99H2mGr/zxczn843qrq+7ho6ODjZs2EBRUZEnhBZCnPMjSS1e2g1B2/BIKYfEoEQiEerr6ykpKWHlypVTbk800TDP1BPIokWLPFq87to0M1JfGY+HWCxGXV0doVAo44TcySCRSFBXV4fP52P9+vX4fD7y8/O9E4gmkOzdu3fCqdPpQBdy13VZv359TqUPQgiKi4spLi5myZIlRCIR2traOHbsGLZtU1BQQHNzc869FVORmk6dKWtPIxAIjNqR6vDR4SkNwzvSqS7kerQ73mjTMAxKS0spLS1l6dKl3o5027Zt3HPPPVx00UX09PTwwAMP8L73vW9KX8NwlJWVsXfv3iF/19/fP+5FellZmef0k+59coHzemeWTtp0fX09xcXF59j06JOdZisGg8GMHT1GIiFIKamoqGDFihXTZhacLQ3VcGZkKBTyivpInpGa+j/hZOYsQdtD6UI+1vOPljqtC3cmJ+FEIjGtPoupoZqrVq3yvpsT2bNNBqmmublMpx4rfLS3t5eBgYGMWYOTPS5N/5/MaPfZZ5/lc5/7HIWFhRw6dAjTNLnhhhv49Kc/zYoVK7J81CMjdWf28ssv84lPfIIjR44AilC1YsUKBgYGxvyOf+c73+EHP/gBP//5zwF45ZVX+PjHP87hw4e927zlCSDpFLM9e/YQDodZsmSJ93faVLW4uJg1a9Z4vovZoN6fPHmSxsZGysvLiUQi55wcc31FcvbsWfbv3z8p6vtY0MxI7RlpmqbXkZaWltLT00NDQwPz58+fFuq//mwzzUFLJZCkWjQN1+qNhun2WdQXaX6//5xCmtqRtre3e3u2yWbPpUIHS+o8rqm8kNPho8ePHycejxMOh4doEafiu6jJTpq1memO+LXXXuOWW27hX/7lX/j4xz+O4zi8/vrrPP3003z0ox8dsoPKJVKLmW3bzJ07l4cffpjbbruNO+64g+bmZp5++mlA7cbC4fA5n3lHRwfz5s3jueee46qrrmLz5s0sXLiQRx991LvNhWKWRjHbv38/hmGwfPlyQGke9Ml28eLFQPasqTRjbN26dR5jT++hNLtO2zNlOydK7/6OHz8+qoYp20gdtba1tWHbNq7rMm/ePC699NIp70i6urpoaGhgwYIFLFiwYNInr+EWTVqrN1pHqn0WZ86cyfLly6e8kMfjcXbu3Onl0KXTkQ7Xs+muLZP9UmpHWFVVNWWu8xqpzhrr1q0b4h0JDKH95+LYUr0eJ+oskorf/OY3bN68mS984QvceeedU/49SkVqMQN46qmn+NCHPkRhYSGO47B9+3Yvy3HBggU88sgjI+71vva1r3HvvfdSXFxMfn4+b7zxxhDnmbd8MRsrbVrj0KFD2LbNypUrOXnypKdz0rsTTfSYjKOHbdveWGUsj0PNrmtra6Onp2fCV/2jIdXjcTrMgnUhPXbsGOXl5QwMDBCLxTx2XXl5ec47Uu2qsXz58pxExOuOVJ/8DcMYsiPVo9V58+Z5lOapRDQaZefOnd6OdqIdYeqONJMMM51MLoSgsrJyyguZ3n/39/efYxGVGj6aOkqecLDqONA6vskUsl27drFp0yYeeughPvnJT05rIRsNzc3N7NixgyuuuGJCF82NjY0cOHCAq6+++pxz1IVilkYxO3r0qDfTTdUZZSuDLBqNekSHNWvWpD1WSd1DdXZ2kp+f73VsE6Ee60Iaj8enLJk4FamBlrqQar2XLtyphsG5SC7WYuyp7khTo1CklMyePZtly5ZNi8/lzp07s+a8n5ph1tHRMe6ezbIsdu3aNeJocyownGwy3oXTcAuqbISP6kI23H1/Iti9ezc33HADDzzwAH/91399XhayXOFCMUuzmJ04cYJwODyE6CGlnFQ3Bnj7oVmzZrF06dKMi6Jt20OyywKBQFpaNs0YzEV8STrQ1PNIJDJmRzrSVX+qZ+Rk4nP0SSSXYuyxcPbsWfbu3Ut5eTnRaDTr9lPjQQv9L774YhYvXpz1E+B4ezYpJTt37iQcDrN27dop3xHqYMtIJJJRjMrwwu3z+YYU7nQKs85DW79+fcaFbP/+/Vx//fXcdddd/N3f/V3OCtkTTzwxov3U448/zkc/+tFR77dp0yaeeeYZ78/XXHMNL774YtaO60IxG6eYDQwM8Jvf/AaAt7/97Z7mLBuFTBMtsp3KrH0HNbtOCOGd+FOviqebMahzyPRYaSIdaaphsGZGzpw5c0LefHq02tnZSVVV1ZSL0WFkn0VNrU41e04dJWfzJJVuqGa2MNKeTQjh7ehyKYgfCZMtZCM9XmrHbVnWkMI90uPrdPSampqMnV0OHTrE9ddfz5/92Z/xhS98IacdWSKRGFI4BgYGqKqq4o033hhRKK0xd+5cXnjhBc+Gz+/3Z/XzfssXM9d1sSxrxH/TRI+ysjLi8TiXXXZZVogeqcm0q1evzulYS1v86HGd4zjecv7EiRMsWrQoK0SHiUK7/hcUFKSlYRsNOk1bnzyGMyNHK9CpHWF1dfW0jFbT8VkcXri1e0w22HWZhmpmC7FYjN/85jcEg0FM0/Qc4/Xry7WeLdf0/9Tw0fb2dvr7+88JHz158iQnTpyYVCFrbGzk+uuv54Mf/CBf+tKXpvyi9Itf/CInT57kG9/4xqi3aWpqora2lpaWlpwdx4ViNkIxk1Jy6tQpDh8+zKpVqzBNkyNHjnDZZZcBkyN6OI7jWRNVVlZm/AXOBHqJffToUbq6ujxTVn3ymKoRY29vL/X19cyePTurrv/DmZGpQuby8nKvYFqW5VkATaQjzBYy9VnU7jH65AgMIZBM5IJAC/VXrFgx6VDNTBCNRtmxY4cXISSEGHVcN96FSSZwXZeGhgbi8Tg1NTVT8h0Yzmw1TRPbtr1g00xe34kTJ7juuuvYvHkzjzzyyJQXslgsxvz583njjTc8tuJI2LJlC3fccQeBQIDu7m42bdrE17/+9aymLlwoZsOKmeu6HDhwwCMjlJSU0NvbyxtvvEFpaSmzZs2alBBWOzpUVlZOuTWTFmKeOXPGC9PUJ/7BwcEhnoq5Yg7qZOJc54ClCpnb2to8ZmRJSQnNzc3eWGs6iAb6Yqa6ujrj73yqqW5bWxuJRCLttHAdYTMdWWCQHtlk+J5tNJeOTOA4jhdqO9U6No0TJ05w9OhRZsyYQW9vb0b5c6dPn+baa6/luuuu42tf+9qUFzJQYuatW7eydevWMW/3T//0T2zfvp2HH34YwzC4/fbbqaqq4utf/3rWjuUtX8yklCQSCeBNarD+kodCIU8Ira+qWltb6evro7i4mFmzZqXNrBsYGKC+vt4Twk71SVTnq/X391NVVXXOrFrbF2mhby6Yg01NTRw6dIhVq1Yxe/bsrDxmuhgYGKCpqYmmpiaklJSUlHgXJlPlt5fqs5hN1uhIaeH68xv++vSObjoibEB9Djt37mTu3Llph6pqlw79+iajZ9OCbNu2qaqqmpZCdvr0aRobG6murqa4uDgjvV5LSwvXXnstV199Nd/85jen/HyisWHDBj772c9y/fXXT+h+27dv59Zbbx1iUTVZXChmyWKmrxYLCgpYu3atR/QYaT+mXQJaW1vp6emhsLDQK2wjvYbOzk52797NvHnzcsIWGw+aaAFQWVk5btelX19bWxvd3d2jpk2ni9Qd4XQEOsKbRId58+Zx0UUXeSeO7u7urDEjx0Kqz2KuT6Ka+Zn6+mbOnIlt2zQ3N1NdXT0trE3Nmpysjm7460t3z3Y+FTI99RkJI72+mTNnekLujo4Orr/+empra3niiSemrZA1NjayYcMGWltbJ/xeNjQ0UFlZSSwWy9qE6kIxk5KWlhbq6+u5+OKLWbp0KVLKtIkeWuvV2tpKV1cX+fn5XmErKCjwupHp2k1os+BMO0JNQNCvT9v7VFRUpLWg12Pbrq6uaWMMjpVMPRIzUu9pspVaPJ0+izq/7Pjx40QiEYLBoNeRjpTSkCv09vaya9eurLMmx6LFl5WVea/PcRzq6+s9H9WplqDAm13xRC4mdNTL2bNnuemmmzxZw5w5c3j22Wen3NwgFV/84hc5ePAg3/3ud8e97a233sr999/Pxo0bAfjWt77FQw89lFVCyFu+mMViMV566SWv2EzG0UP/sFpbW+ns7MQwDFzX9Ra8U92RdXd309DQwEUXXZT2SGcsDNey+f1+KioqmDVr1ogn/ukWY4NyGjh48CCrV68eYn0zElLjebRDx0iSholgun0WU0MtKysrh5AQpJRDnP5zVWS7u7upr69n0aJFOd2TphKAUvdsM2bM4MyZMwDTYpEF6nt46NAhqqqqMp5MnD17lj/90z+lp6eHeDxOc3Mz7373u/noRz/KLbfckuUjHh9vf/vbuf3224dozkbzVvzc5z7H888/zyOPPEJ7ezt/8Rd/wV/91V/x0EMPZe143vLFDNQHEAgEsubooU/imorb3d2dtog5W9BL/mXLlnm6jmxiPC2bZgxqR4fp8NjT+p1169ZRVlY2ofun6oW0pGGiES/T7bOou+Lu7m5qamqG7F5GSmnQeqhsEoC6urqor6+fcvq/3rO1trZy+vRpHMeZlj0pwJkzZzh48OCkCllPTw+bNm1izpw5bNmyBb/fz4EDB3j66acpKSnhE5/4RJaPemxEo1FKSkpoaGjwPGthdG9Fy7K44447+OEPf0hFRQW33XYbDz74YFbPCxeKGYoy6zgOjuNM2vFeO2oEAgGPMTj8ij8106y0tDSrJzl9Ej9x4gRr166lvLw8a489GoZr2WzbRkpJcXEx69atmxbqu7bHmgj1fazHG86MHC/FoLe3d1p9FrUYeHBwcFwdnbYO04W7v7+f4uJi7/Vl+rvs6Ohg9+7d3mRiqmHbtifBWL58uceOTN1DpTsuzxS6kFVWVk74gkqjr6+PzZs3U1xczNatW6dlwvG7gLd8MTt06BAvvvgi733ve5k5c+akOrK+vj7q6uq8K/GRHktTjvWJUcedz5o1a9JaGn0lrh0tplLDpqGvxAsKCkgkEsTj8SFar1wXNn0SHxgYoLq6OidX4KOlGOgrfi1GzrazS7rQRAfNyp1ol6UJQFoPlcmJX+vYpoO5Cm8WMsMwqKysHDJCTd2zdXZ2ekL74Xu2yaKlpYUDBw5Mijk6MDDALbfcQiAQ4Nlnn53ypOvfJbzli9mrr77Kpz71Kerr63nb297G5s2buemmm5g1a9aErtZaW1vZt2+ftxdIl3KcKvLV7hyzZs2asAjWsixPOzNd+yn9HixdupSLL77Yu+JvbW31tGy6o6moqMi6lk0zBh3HoaqqakqSaIczP4PBIPF4nMWLF0+Ls4o+iUN29kOagKD3pD6fzyvco118nT17ln379k2bjs22bXbt2oVpmucUsuEYPk7Olp5NW9VNppBFIhFuvfVWpJQ8++yz00Ke+l3CW76YgSoqJ0+e5Mknn2TLli288cYbbNy4kZtvvpmbb76Ziy66aNSTUmoG2OrVqzP+8abuMFpbW7Esi/LycmbNmjXEvWIkpLruT4dZMMCpU6dobGwc03V+uJZNa/WyscOIx+Ps2rWLYDA4La7rgBcPVFRURH9/v2c9NVV70rFCNbOBVCHzcIcVvUfUY7WpSh8YDr2r9fl8E34PRkqdHk2vNxZ0lNC6desyHvPHYjE+8IEPMDg4yE9/+tOcsxbvvvtuvvrVr3p/Xrx4MY2NjWPeZ/v27dxxxx20t7fz4IMP8qlPfSqnxzgeLhSzYZBS0tzczJYtW3jyySd57bXXqK6uZvPmzdx8881Duq5YLMbBgwfp6+ujsrIya1+4VJFoa2ur516hC1vq1aIebWo3helgy2lXER2Nkw6GdzQFBQWepGGiWrbBwUF27dpFaWlpRjlck8VIPosjMSNTraeyfYyxWIxdu3alFaqZDaTuEXW+V15eHpFIxMv6m2pkO0ZmNL3XzJkzRwxWhTcL2dq1azMu5vF4nA9/+MN0dHTwwgsvTIkm8IorruBv//ZvueKKKwAwTXPMNUV7eztLlizhvvvu44Mf/CB//Md/zMMPP8w73/nOnB/raLhQzMaAlJLW1lZ+/OMf8+STT/KLX/yC1atXc/PNN3PVVVdx3333UVlZyb/+67/mdKyn3R1aW1u9Ud2sWbMwDIMDBw5MaLSZTegMqL6+vklZM2ktlNZ6TUTLpokWc+fO5dJLL53y9yAdn8VsMCPHgg7VLC0tZcWKFdNia9TY2MjJkycJh8NEIhGKioq8jmYqnPB1IdNavmy/B+ns2fSecDKFLJFIcNttt3H69GleeumljEkjE4Ft25SVlXHmzJm0R5mPPPIIjz32GAcOHEAIwdatW/nhD3/I9773vRwf7ei4UMzShJSSzs5Otm7dyne/+11+/etfs3jxYm666SZuvfVWzyw119CjutOnTxOLxSgoKODiiy+moqJiSr0ec7Wf0mnM+opfa9kqKirOcYnXbLlc+zyOBu2zqKnv6Xx/h3c00Wh0XGbkWMh2qGYm0GN2bc+UqmXr7OwkLy/P60pH62gmA8uy2LlzpzdiznUxHynmpbCwkN7eXlauXJkxc9O2bT72sY9x6NAhXn755Skb0+7atYurr76aWbNm0dzc7FlkjUVeuv322wmHw3zta18DFNnlmmuuYf/+/VNyzCPhQjGbIF555RVuueUW/vRP/5TKykqeeuopXnjhBebPn8/NN9/M+973PlavXp2zH5TuBFpaWlixYgXxeJzW1lZ6e3s9OnVFRUVOWU96R6fDFHO1n3Jdd0hh08zPiooK4vE4Bw8eZOXKlcyZMycnzz8WsuWzOJwZOZHPsK+vj127duUsVHM8aJuy06dPU11dPeKYPfXipKOjI+vjVu2uovfF0zFi1gkboVCIeDye0Z7Ntm0+8YlP0NDQwMsvvzylY9rvf//7PProozz66KOUl5dzzz33YNs2zz///Kj3ef/738/GjRt54IEHAPU9njt3Lr29vVN12OfgQjGbADo7O7n00kv5l3/5F/7sz/7M+/u+vj6eeeYZtmzZwk9/+lNmzZrFzTffzObNm6murs7aD0ybBeswvNT3Kx6PeyfFbPgpjgYd6Dlz5swp3dGlatlaWlq80ci8efNy6l4xEnLlszjSHlGf+AsKCoYUK+01uXDhwjGjN3IFKSWNjY2cOXOGmpqatMZT2WYOJhIJdu7cSV5e3pTsCUdCR0cHDQ0NnsNMJns2x3G46667eP3113nllVemRZOXipMnT7Jo0SK6u7tH5QF84AMf4G1vexv33HMPoF5DKBQaNRtyKnChmE0QHR0dYzKUBgcHef7553nyySd59tlnKS0t5aabbmLz5s1s2LAh45NuPB6nvr4ewzBYt27dmOMo7Repd1DaiHXWrFmTMtLVhskLFiyYFtq5Jps0NzezdOlSb+Qai8WmTMs2VT6Leo+oPQdTmZHaYWa6QjX1dKC1tZWampqMzaeHO+GXlZV5J/7xOl1dyPLz83M6CRkLWk+4cuXKETupVFnD8D1baWkppmniui733nsv27ZtY9u2bdOiSxyO3t5eSkpKOHjwIMuWLRvxNn/5l39JeXk5n//85wF1cXXRRRcxODg4lYc6BBeKWQ4RjUZ54YUXePLJJ3nmmWcIh8PcdNNN3HzzzVxxxRVpL/4HBgaoq6ujpKSElStXTugEatu2V9g6OjoIhULeSXEi+4szZ85w4MCBaTNMdl2Xffv20dvbOyTCRmvZdFc6MDAwZAeVzT2i9lksLCyc0hNoKjNSE0hKS0tZsGBBTpiRY0FK6Qnz090TpoNIJOJ9T3t7e73JgiaQpH5Pz6dCtmLFirTG3MO70jvvvJP58+dTWFjIzp07efXVV7NqwDwRfOpTn2Ljxo380R/9EQAvvvgi1157Lf39/aN+vt/5znf4wQ9+wM9//nNArV8+/vGPc/jw4Sk77uG4UMymCIlEghdffJEnn3ySrVu3YpomN954I+973/u46qqrRu0murq6aGhoyEp8jOM4nlFwKrliNKNgGEo7X7t27bRkYOlORAvCxypQ0WjUO+lnc4843T6LoJbsWpivu2/btr1Q1fLy8pxqDKWUQwgvudrLDk8ySO1KQ6GQd0ExHcbN8KbLTaY2Xa7r8vrrr/Ov//qvvP7660QiEa688kpuvvlmbrrpJhYtWpSDox4d3/3ud/n85z/Pt7/9bWzb5s477+SKK67g29/+9qjGwR0dHcybN4/nnnuOq666is2bN7Nw4UIeffTRKT32VFwoZtMAy7LYvn07P/rRj3jqqaewLIsbb7yRzZs38453vMM7WT/11FPk5+ezcuVKLrrooqwew0jkCl3YdDSI67ocOnSI9vb2abPH0kJgLYKdyMl6+B4xNbdsIm4K0+2zCCoH68iRI0McJVJDHdva2ohEIp5ZcLYdVrQMQ9uETZXDjO5KU/ds4XCYpUuXTvmuFCZfyEB9bp/97Gf5z//8T7Zt20ZeXh5PP/00W7duJRgM8vTTT2f5qMfHZz7zGR577DEKCwt53/vexxe/+EXy8/NHNQ4G+NrXvsa9995LcXEx+fn5vPHGG+MmU+QSF4rZNMNxHF599VWefPJJfvzjHzMwMMD111+PlJKnn36a5557jtra2pweQ2p0RltbmxcNMjg4iG3bOfM4HA/ZHOsN17KlO26dbp9FwDOOHivQEd5kRra3t3sOK9noSrXfZSQSoaamZkpswoYjFouxY8cOwuEw+fn5tLe3k0gkPALJzJkzc+772d3dTV1dHcuWLcv44lJKyT/+4z/yzW9+k5dffpnVq1cP+Xedofi7gsbGRg4cOMDVV189rdlqcKGYnVfQhe3OO+/k2LFjzJ49m/Xr13PzzTdz7bXXTon4VEpJe3s7Bw4cwLKsIZleU3kl3N/fz65du5g1a1bW9VOp49ZUv8HhWjbt5jBd9H8pJUePHqWpqYmampoJdcbDmZGaBDQSM3IsOI7jZdLV1NRMSzpzLBZj586d3s5YCIGU0jMTmIz1VLro6elh165dnu9oJpBS8uUvf5lHHnmEl19+mXXr1mX1GN/quFDMziP09PRwyy230Nvby9atW2lpaeFHP/oRP/7xj70gvptvvpnrr78+Z1dBkUhkSJhkqvuIvhLO9X5G7wmngjU5PMUAoKKiAsMwaG5unpSbw2SQGqqZKWNQQ7tX6OIdDAa9UeRwIXoqUtOZsylBmAh0R6atykY71uGU+LFkDROFlkEsWbIkY/aolJJHH32UL33pS/zsZz/L+bTlrYgLxew8wnPPPcc3vvENvv/97w/Z6biuy+7du/nRj37Eli1bOHbsGO9617u46aabuOGGG8Y8IU0EY1lD6Sth7YAfjUY94kE2Rzy6G1q+fHnW94TjQacYNDY20tvb61GpdfGeqq5UO4v09PRknWiRuoNKFaLPnDmTGTNmeCOu1CywysrKaTGv1jZdZWVlE3LYSS3enZ2dHtFp5syZ3j44XfT29rJr165JF7JvfOMbXtry5ZdfntHjpIutW7fyyU9+klOnTlFTU8MTTzzBihUrxrzPpk2beOaZZ7w/X3PNNbz44os5Pc5s40IxO88gpRzzR6sZZbpj279/P+94xzvYvHkzN954IzNmzMiosLW3t7Nnz560d0Op0S6pdPjJEA80yWG6HNe1jq2lpYWqqiqklEMCOXNRvIcjNVSzpqYmpxZlqUJ0bctUXl7OjBkzaGpqypn7fjrQhWzGjBmTYo/qRHRdvPU+OJ2xuS5kixcvznhfKqXk8ccf58EHH+TZZ5/lqquuyuhx0sXRo0epra3lscce4+qrr+buu++mubmZX/3qV2Peb+7cubzwwgveCNXv90/JWiObuFDMfoehT766sNXX13PllVeyefNmNm3alHYmW1NTE4cPH2bVqlUZsZGGR7vo3YWmUqfzOvRuqLKyckpcwodDB5t2dXWNqJ/S41ZdvEtLS73XmK2Co0M1Lcuasjw2DS1ibmlpoampCdd1hxTvqfT9jEaj7Nixw3OZydaYOTVmqa2tjXg87rE/h/ti9vX1sXPnTs/EO9Pn+973vsf999/PT37ykylxlH/mmWdoamrijjvuAGDbtm1cd911xOPxUe/T1NREbW0tLS0tOT++XOJCMfs9gdaD6Uy23/zmN1x++eWedmWkTLZcFJFYLOadLHp6ejz39FmzZo04LkstIlVVVdMSQDhRn8VcaNksy6K+vh7ITqhmJojH454YefHixd6oLpvMyPEQiUTYuXNn1gvZcGixvSbJpPpi5uXlsW/fPm9nm+nj/8///A933303W7Zs4T3veU92X0CaeOyxx3j00UfZt2/fqLfZsmULd9xxB4FAgO7ubjZt2sTXv/51SktLp/BIJ48Lxez3EFJKmpqa2LJlC1u2bOG1116jpqbGCxudP38+8Xicz3/+87zrXe9iw4YNORkpJBIJ76Tf1dXl6by0rZZmykWj0SnVLqXCtm3q6+sz9lnUDvHDX6P2xEznZDxVFlljQTMGNfEnda+k9Xrt7e10dXVlzIwcD5FIhB07djBr1iyWLl06pXo+zf5saWmht7eXQCDARRddlFYM0UjQBeK///u/ueGGG3J01GMjkUiwcuVKPvnJT3LnnXeOert/+qd/Yvv27Tz88MMYhsHtt99OVVUVX//616fwaCePC8Xs9xxSSs6ePTskk23VqlXYtk0sFuOnP/3plNhTjaTzchyHQCBAdXX1tGiXsl1EhrMG09Gy6VDNgoKCabNmSs1DG4sxCOeSKwKBQFrMyPGgo2xmz549Lbl0oEbJO3bs4KKLLqKwsPAc6Yb2VBzvM3r66af52Mc+xve///0RxcZThU9/+tO88MIL/Pa3v53QRdr27du59dZbaW9vz+HRZR8XitlbCFJK9uzZww033IDruvT397NgwQLP4X+qbJq0NRSozigQCHgp07nIuxoJufZZHJ40bZrmEC2bYRieDCKdIpIr6JTu8vLyCX/+mlwxPKJnODMynWPYsWMHc+fOZcmSJdNayLRtnIaWbugLMdd1xwxWff755/nIRz7C448/zh/+4R9O9cvw8POf/5z3v//9/PrXv2blypUTum9DQwOVlZXEYrEp3ZVOFheK2VsI+/bt4/rrr+dd73oXjz32GAMDA/zkJz9hy5Yt/PznP/cK2/ve976c+d7pQqZPnjr0VJ8QRxMw5+IYpspnMVXLphl1paWldHV1MXv27GnzehwYGGDnzp3MmTNn0t2QZkbqk75mRo6nSdTHMJ2FTBdTnQs3GoYHq0YiEUpLS/nVr37F5s2bOXLkCB/84Af55je/yQc/+MFpeS0Ax44dY+PGjfzbv/0bH/7wh8e9/a233sr999/Pxo0bAfjWt77FQw899DtHCLlQzN5CeOWVV9i+fTt/93d/d84Prbe3d0gm25w5c7yOraqqKiuFTYtPL7nkkhE9DvVJv7W1dYhfZEVFRVrjnXQw3T6LUkqam5s5dOgQhmEgpfTGdCNd6ecK/f397Ny5MyfBnqPFuwxnRupCdtFFF01LuCi8WcgyOYbBwUEOHTrEHXfcwYEDBygoKODaa6/l85///KjRKblGNBqlpqaGK6+8ki9/+cve3+fn59Pf3z+iabDWvz3yyCO0t7fzF3/xF/zVX/0VDz300FQf/qRwoZhdwDkYGBjwMtmee+45ysrKvEy22trajHZLbW1t7N27N+0MLn2lr7Vsw0/6mRS288Fnsbu7m/r6ehYuXMj8+fO9k34uhejDofVT8+fPnxKH9uHSjeLiYoqLi2lubh71wmYqkK3x5q9+9Ss+8pGPcM0119Dd3c2LL77IwoUL+fSnP83tt9+e5aMeG0899RTve9/7zvn748eP8453vGNE02DLsrjjjjv44Q9/SEVFBbfddhsPPvjgtDBqJ4MLxewCxkQkEhmSyZafn+9lsl1++eVpfeGbmpo4dOiQl8Y7UWh9kC5slmVN2Jljun0W4c1iOpq/38DAwBCqeC60bLo7nox+ajKIx+OcPn2aEydOIKU8J8lgqoqaZk5OlnDym9/8hptvvpl/+Id/4M4770QIQX9/Pz/72c8oLi7m3e9+d5aP/AJGw4VidgFpIxaL8dJLL/Hkk0/yk5/8BJ/P52WyXXnlled0ElJKjh8/zsmTJ1m3bh1lZWWTPobUvcXwlOmZM2eOWFy1KHy6nEVAdaZ79uxJu5hqr8HW1lZ6e3s9vZ7WQWUCHV8yXQnV8OZ485JLLmHevHl0dHR4adradiqX+1J4U8tWUVExKQnArl272LRpEw899BCf/OQnp21HdgEKF4rZBWQEy7J45ZVX+NGPfsTWrVuxbXtIJpthGHzqU5/iyiuv5Prrr89JFpoWvuqObXBw8JwxnQ4WraysnDYR6JkzZzh48CCrV6+moqJiwvcfrmXLROelu8LJxJdMFn19fd54c3iq8nBmJOB132VlZVnT3mXLXWT37t28973v5dOf/jR//dd/faGQnQd4SxWzzs5O1q9fz7Zt24Yo+/fu3cvtt99OY2Mjf/7nf86XvvSltL6c27dv54477qC9vZ0HH3yQT33qUzk8+vMXtm3zy1/+0gsb7e/v55JLLqGrq4stW7awZs2aKTkOneelx3TBYBDLsoYEWk41RgrVnAxGcsAfT9bQ3t7O7t27p3XEqu2hFi5cOK6rhpTS84xMZUbOnDmT8vLyjHeJ2Spk+/fv5/rrr+fuu+/moYceulDIzhNMRTE7L5LmOjo6uPHGGzlx4sSQv4/H42zatImamhp27NjB/v37eeKJJ8Z9vPb2dm666SY++MEP8vrrr/P973+fbdu25ebgz3P4fD7e8Y538NWvfpXdu3ezePFiOjs7KSgo4N3vfjcf/ehH+fGPf8zg4GBOjyM/P5+FCxdSW1vLzJkzsW2bvLw86urq+O1vf8upU6eIRqM5PYZUHD9+nMbGRqqrq7NWTP1+P3PmzGHdunW84x3vYOnSpcTjcXbt2sWrr77KwYMH6erqwnVdQO0Kd+/ezerVq6etkPX29no+h+nYQwkhKC0tZdmyZVx55ZXU1taSn5/PiRMn2L59O7t27aKpqWlMv8Hh0A4n5eXlkypkhw4d4sYbb+TjH//4lBWyvXv3UltbS2lpKQ888ABSjt8bbN++nRUrVlBeXj6E1XgBk8N50Zm9613vYtOmTdx7770cP37c+1E99dRTfOxjH6OpqYm8vDwaGhq48847+eUvfznm4z3yyCM89thjHDhwACEEW7du5Yc//CHf+973cvYaznecPXuW6667jrlz5/LDH/6QcDjMjh07PCPkM2fO8J73vMfLZMvF6HEkn0Vtx6SDKgsLCz1brVx856SUNDY2cubMGaqrq3PyOodjpLTw/Px8ent7WbNmzbTF2WvmZLYIJ5oZ2d7envYuUWeiTTRKZjgaGxu5/vrr+dCHPsQ///M/T4lbSzweZ/ny5Vx77bU88MAD3HPPPdx6661jsiTb29tZsmQJ9913Hx/84Af54z/+Yx5++OEpMTqeTrxlxozHjh3zKMCpxeyzn/0sb7zxBs899xygTkQzZsygq6trzMe7/fbbCYfDfO1rXwOgpaWFa665hv379+fsNZzvaGtr49/+7d/43Oc+d84oyHVdGhoavMJ2/PjxIZlsxcXFk77KTcdnMZFIeMSK1P2T9ouc7DFIKTl48CDt7e2TDtWczDE0NjZy8uRJ/H4/juNMSajqcGjm5GQiVMbCSLtEvWfTfoojpVRnghMnTnDdddexefNmHnnkkSmzHcvkYvuteqH9e1XMNm/ezCuvvHLO33/hC1/grrvuUgczrJjdd999xGIx/v3f/927/cyZMzl8+PCYhIH3v//9bNy4kQceeABQ+5q5c+fS29s7qdfwVoCUkn379nmF7eDBg0My2crKyiZ80snEZ1Hvn1pbWz2/SL1/ysRcNpehmhOB3tNp0stwLVuqgDlXnpjZSGeeCGzbHrJL9Pv9zJgxg46ODkpLS1m9enXGhez06dNce+21XHfddXzta1+bUv/MTC6236oX2lNRzKZMefeNb3xjxJ3IWJRwn893joYnFAp5VjXp3k/f5wLGhxCC1atXs3r1av7+7/+ew4cP8+STT/Ltb3+be+65h6uuusrLZKuoqBj3JJSpz6LeP82ZMwfbtuns7KS1tZUdO3YQCAS88VU6XaMO1YxEItTW1k6bp92JEyc4fvw41dXVXqRPUVERRUVFLFmyxCPJNDU1ceDAAU/LNnPmzKylFnR3d1NXVzelEgCfz8fs2bOZPXs2juPQ2trKoUOHcF2Xzs5O9u/fnxEzsqWlhRtuuIFrrrmGf//3f59yI+i+vr4hzE8hBKZp0t3dPer5qa+vb4gfY1FREc3NzTk/1rcCpqyYZbIXKCsrY+/evUP+rr+/f9wr1rKysiGu0unc5wLOhRCCZcuW8eCDD/KZz3yG48eP8+STT/KDH/yA++67b0gm29y5c88pKtnyWfT5fMyaNYtZs2Z5NPHW1lbq6uqGmASXlpae8xyO41BfX49t26xfvz5nzh3j4dixY5w6dYqamhqKiopGvI0mySxcuHCIlu3QoUNZ0bLpQjaaMHwq4DgOJ06coLy8nFWrVnmBnAcPHsSyLE++MR4zsrW1lRtuuIHLL7+cb37zm9MSzZPJxfaFC+3c4bz2RKmtreVb3/qW9+cTJ04Qj8fHFfjW1tbygx/8wPtzfX39tOl3fl8ghGDRokU88MAD3H///Zw+fdrLZPubv/kb1q9f72WyXXLJJWzfvp0nn3ySe++9N6uWSKZpeu7vmlihWYGAd8IvKyvzCpkQgpqammmxAEoNWa2pqUmbcBIOh7nkkku45JJLvF1iW1sbjY2NGWnZtCh7OrVsiUSCnTt3UlBQ4Jlll5aWUlpaytKlS73E8BMnTrBv3z7Kysq8PVtqAWhvb2fTpk1UVlby+OOPT0shg8wuti9caOcO5wUBRGP4zsy2bebOncvDDz/Mbbfdxh133EFzczNPP/00oFr2kcw5Ozo6mDdvHs8995w3Flu4cCE1NTUjMo0ef/xxPvrRj455bJs2beKZZ57x/nzNNdfw4osvTu4F/x5ASklLSws//vGP2bJlC7/4xS9YsWKFpwv8x3/8xymhSEsphzAGHccBVFGYrkw2KSWHDx/m7Nmz1NTUZCWpeyQt23gjV13Ili9fPiX5eCNBF7L8/Py0xs2RSMQr4L29vdTX19Pb28t1113Hfffdx5IlS/jv//7vaeu0AV5++WU+8YlPcOTIEUBdbK9YsYKBgYFRC+x3vvMdfvCDH/Dzn/8cUAbjH//4xzl8+PCUHfd04PeKAJIOhhczUIyhD33oQxQWFuI4Dtu3b2fVqlUALFiwYERzToCvfe1r3HvvvRQXF5Ofn88bb7xBaWnpkDd1YGCAqqoq3njjjXFNXefOncsLL7zgjWf8fv+0sOHOZ0gpefzxx/nLv/xLqqqq2LVrFytWrPAc/iejIZoItADXMAxc10078iSb0MzJjo4OampqcvL7GZ7LZhjGOUkG2l1kOguZZVns3LmTcDjMmjVrJrzbisfj/OhHP+Lb3/42O3fuJBQKcdddd3HrrbdSXV09bcLosS62J3qh/eijj07La5gqvOWK2Whobm5mx44dXHHFFRPy72tsbOTAgQNcffXVI+4pvvjFL3Ly5Em+8Y1vjPk4TU1N1NbW/s5lCE01/uM//oNPfvKT/L//9/+44YYb6O7uZuvWrV4m26JFi7xMtpUrV+ZkYT88VBOYcvd7KSX79++nu7t7ypiTI2nZCgsL6enpYfny5dM2WtSFLBQKsXbt2ow/876+Pm6++WaKioq47bbbePbZZ3nuuecoLS3lpZdeYsmSJVk+8vQw2sX2RC+0p0trOFW4UMxyiFgsxvz583njjTfGdT7YsmULd9xxB4FAgO7ubjZt2sTXv/71afMTPF/x1a9+lbVr1/L2t7/9nH/r7e3l6aefZsuWLfzsZz9j7ty5XsdWWVmZlcKmM7hmz549qkmt3su0trYOyfKqqKjIyijSdV327dtHX18fNTU1WWMhTgRSSk6ePEljYyM+n29IAvNUatksyxoiycj0Mx4YGOCWW24hGAzyzDPPeBcH8Xicl19+mXe/+93TGomSycX2eBfav2+4UMwyRDqatu985zts3bqVrVu3jvt4//RP/8T27dt5+OGHMQyD22+/naqqKr7+9a9n+9DfEhgYGOC5557zMtnKy8uHZLJlctLTRrkTCfbUjhWtra309/dTUlLCrFmzMqbCp0oAqqurp00C0N7e7qUAzJo1yyvgIxk+52qXaNs2u3btwu/3T6qQRSIR3v/+9wPw7LPPZmXveAFTjwvFLEO0traOqmnTV0EbNmzgs5/9LNdff/2EH3/79u3ceuutQ1hJF5AZIpEIP/vZz3jyySe9k9WmTZvYvHkzl19+eVpMNR2qORlbplgs5hU2bcWkRdrpjAkdx2H37t3E4/FpI5zAm8bFo+XTDTd8Likp8TrTbHWRupD5fL60RfIjIRaL8YEPfIDBwUF++tOfviU6mN9XXChmOUJjYyMbNmygtbU1o51JQ0MDlZWVxGKxabv6/n1ELBbjxRdf9DLZAoGAl8n2tre9bcTPqqOjg927d2dVO6WtmFpbW+nu7qagoMArbCORfrQEwHGcUa26pgI6ly3doFVdwNva2ujp6fF8MUd7nenAtm3q6uowDIPKysqMC1k8HufDH/4wHR0dvPDCC57IfCqwdetWPvnJT3q6wCeeeIIVK1aMe78LjOfRcaGY5Qhf/OIXOXjwIN/97nfTuv2tt97K/fffz8aNGwH41re+xUMPPXSBEJJDWJbFtm3bvEw213W54YYbeN/73sfVV19NIBDg//7f/0t/fz+33nors2fPztlx6MLW2dl5jsZLFzIpJVVVVdO2u9Fp3WvWrMkoly1VyzbS60xnbOs4Drt27Zp0IUskEtx2222cPn2al156KSvBseni6NGj1NbW8thjj3H11Vdz991309zczK9+9atx73uB8Tw6LhSzHOHtb387t99++zmas9HotJ/73Od4/vnneeSRR2hvb+cv/uIv+Ku/+iseeuihcx777rvv5qtf/ar358WLF9PY2DjuMV3IXxsdtm3z6quveplskUiEDRs28Itf/IKvfOUr/Mmf/MmUHYc+4WuNl+u6BIPBaRNlw5uFbO3atVlJ6x7upZiOfZjjONTV1QFQVVWVcSGzLIs/+7M/49ChQ7z88stTnj7+zDPP0NTUxB133AHAtm3buO6668aNtLnAeB4bF4pZDhCNRikpKfG0N6kYjU5rWRZ33HEHP/zhD6moqOC2227jwQcfHPHkdcUVV/C3f/u3XHHFFYByrBjP9eGtGguRCRzH4b777uPrX/86S5cu5dSpU1x33XXcfPPNvOc975my76nWskkpsW0bv9/vnfBLSkqmTPt09uxZ9u3bl7VCNhzDU6aFEOdo2XR36rou1dXVGRcy27b5xCc+QUNDA9u2bTsv6OqPPfYYjz76KPv27RvzdhcYz2PjQjH7HYNt25SVlXHmzJkJsa7eqrEQE4WUkn/8x3/k4Ycf5vnnn6e2tpbf/va3nsP/2bNnvUy26667LmdZZTpwMy8vz0vqThUvj3TCzwVaWlo4cOAAa9eupby8PCfPkYpULVt7e7sXX6MdL6qrqzPuTh3H4a677uL111/nlVdeybnAOx3GcyKRYOXKlXzyk5/kzjvvHPPxLjCex8aFYvY7hl27dnH11Vcza9Ysmpubufrqq/nmN785bl7UWzUWYqKwbZuPfOQj/PVf/zVr164d8m+u61JfX+8VthMnTvCud72Lm2++mfe+971ZyWQDRZrYtWsXBQUFI9oyjSRe1v6CM2bMyFphm+pCNhzaPmzfvn0kEgmAIVq2iZBgXNfl3nvvZdu2bWzbti0n+WrDkQ7j+dOf/jQvvPACv/3tbydM6sk24/k///M/+ed//mfPC3JgYIDy8nLPpux8x4Vidp5itKu6T37ykzz//PM8+uijlJeXc88992DbNs8///yYj3chfy27kFKyd+9er7AdOnSId77znWzevJkbbrgho0w2UKPFnTt3eu4i4z2GlJKenh6vsNm2TXl5ObNmzWLGjBkZj+POnDnDwYMHWbduHTNmzMjoMSYLHehqWRZVVVVDmJETEaO7rsunP/1pnnvuObZt2zYkUmU68fOf/5z3v//9/PrXvx4S2ZIuss147uvro6KigoaGBpYtW8YPf/hD/uEf/oH6+vpJP/ZU4EIxO0+RzlUdwMmTJ1m0aBHd3d1jamQ+8IEP8La3vY177rkHUCOXUCiEZVnZP/i3GKSUHDp0iCeffJItW7awZ8+eIZlsM2fOTFtgvXPnTsrLyzOKs5FS0tfX52nZ4vG4V9gm4sqhC1llZeWUsvxSoQtZIpGgurr6nK5Fi9Hb2tro6+sbVcvmui7/+3//b5588kleeeWVabOkGo5jx46xceNG/u3f/o0Pf/jDad1nKhjPmzdvZsOGDTz44IN8+MMfZvXq1XzmM5/J2uPnEheK2e84ent7KSkp4eDBgyxbtmzU2/3lX/4l5eXlfP7znwdUEvBFF13E4ODgVB3qWwJSSo4dO+YVtp07d3L55ZezefNmbrrpJubMmTNikRocHGTnzp3MmjVrVJusiR5Hqq2WTpjW7iOjjbSam5s5dOjQtBey3bt3E4vFqKmpGXf8FovFPAZod3c3g4ODvPHGG/zRH/0RTz31FP/5n//Jtm3bzptRWTQapaamhiuvvJIvf/nL3t/n5+cjhMgK4zlT/Nd//Rdf/vKXef3116moqGDHjh0sXrw4a4+fS1woZr9j+NSnPsXGjRv5oz/6IwBefPFFrr32Wvr7+8d8/96qsRDTCSklp06d8jLZfv3rX1NbW+tlss2bNw8hBL/5zW84cuQIGzZs+P/bu/doKPM/DuBvpNYQkkhllepssusMg6xK21UlYtMeXVZy6rBrs7Wt3U1pj9rsVqL7ii6OTrWrkqKotiR2y6UL64xWhEIuJddI8vz+6Hh+TRhjmGHG53XO/GHM83imc/TxfOf7+bwxbtw4iexSbJ3KUVZWhrq6unaX6IqKipCTkwNTU9Ne2yHXOq6r9T/8rn6O1NTUhH/++QcBAQFITU2FkpISXF1d4eHhAVNT016bfv+u6OhoODk5tXm+Nc2jJ3Y8i6uurg46OjrYvXs3wsLCkJaW1mPnljQqZjImIiICW7duxZEjR9Dc3AwvLy9YW1vjyJEjALqev9ZRLARNKOhZDMOgpKSEzWRLSkoCl8uFtbU1G2mzefNmqcXXlJWVCSzRKSsr49mzZzAzM+v1Qvby5UvweDyxx3UxDIOgoCAcPHgQ69atw7179xAbG4uhQ4di586dWLx4cQ9fuXxZtGgRrl27hk2bNuH777/v7csRGRUzGbRhwwaEhIRg8ODBcHJyQkBAADsFoCdiIWhCgWQxDIPy8nIEBQUhODgYo0ePBofDYSf898Qyo6gaGxuRk5PD7orU0NBg79ik+fvY0tKCrKws1NfXd7uQ7du3Dzt27MCVK1dgbm4O4O37vHbtGvT19dvsUiWCIiMj4eLigoKCAqns+uwpVMz6GVFiIWhCgeTdvHkTCxYswLZt27B06VI2k+2vv/7C2LFj2Uw2IyMjifWQAcDjx4+Rl5cHU1NTcDgcdlNFZWUl1NTUBMZNSUrrztDa2lqYm5t3q5AdOnQIW7ZsQXx8PLtRgoju0aNHSEpKQlhYGJKTk3v7crqEihnpFE0o6FkMw8DGxgYrVqzAqlWrBL5XVVUlkMk2atQo9o6tOzEn7SksLMSjR49gZmYGDQ0Nge+1zotsnaOooqICHR0d6OrqijxHURQMwwhks4m7xbw1gdzX1xcXL17E1KlTe+T6+hsTExOUl5fj9OnTMvdvSMWsH6MJBb3n9evXnW5uqK2tZTPZ4uLi2Ew2JycnmJubd6uwCStk7+tojqKuri7U1dXFLmw9WciOHz8OHx8fxMTE4LPPPhPrPES2UTHrx2RtQkF/9vLlS8THx7OZbOrq6mwmm5WVVZeaowsKCpCfnw8ej9fl/K43b94IjNVSUlJiC1tX5kUyDAM+n4+qqiqYm5t3q5D9+eef8Pb2RlRUFObMmSPWebqDBn/3DVTMSIf62oQC8lZjYyOuXr2KqKgonD9/HoMGDYK9vT2bySZsq3Z+fj4KCwthZmbW7SDKlpYWdkBweXk5FBQUMGzYMOjq6gqdF8kwDLKzs1FZWQlzc/NuBXZGRUXBw8MDkZGRsLOzE/s83UGDv/sGKmakXX11QgER1NTUhISEBJw9exbR0dEAwGay2djYCGymSE1NZbe99/SA5JaWFnasVllZGVpaWtjNI1paWuydY08WspiYGLi7u+PEiRPt7t6VBhr83XdIo5hJbisWkYiGhgYsWLAAjo6OWLhwIerq6lBXVweGefs3SU1NTbtjsExMTLBu3TqkpKQgNjYWfn5++PrrrwVek5WVBQsLCwwZMgQ+Pj7sOYVJTEyEkZERtLW1BSYmEGDgwIGwtbVFaGgoSkpK8Mcff0BFRQWenp4wNDSEh4cHLl26hPXr1+PLL78El8uVyKR/RUVFaGlpYcKECbCxsWFDRB88eIDExERkZmaitLQUfD4flZWV4PF43SpkcXFxcHd3R3h4eK8VMgDIzMwEwzDgcrlQUVHB3Llz8fjx406Py8jIwIwZM9hlWUtLS9y9e1fSl0u6iYqZjLl8+TKys7MRFhaGwYMHs4/CwkIAb4vWxYsX2xy3YcMGTJw4EbNnz8batWvx1VdfCcx1e/XqFezt7cHj8ZCeng4+n4/w8HCh11JRUQEHBwcsWbIEt27dwokTJ5CQkNCj71deDBgwADNmzMDBgwfx5MkTREdHY8iQIVi1ahUiIiJgZWWFxMREif8Fq6CgAE1NTXz00UeYMmUKzM3NoaKiguzsbJSUlIDD4aCqqkrsuaDXrl3DihUrEBYWBmdn5x6++vY5OjpCU1OzzSMmJgbGxsY4deoU+Hw+lJWV4eHh0en5ampqBAYeq6uro7i4WJJvgfQAWmYkAN6O8XF3d0dRURE4HA4yMjLg5eUltJ+FlmPExzAMNm/ejLCwMAQHB+POnTs4d+4cysrKYGtry2aySbKHrPU6cnJyUFZWhokTJ6K6upqdfD906FDo6Ohg2LBhIvWX3bx5E4sXL8a+ffuwYsUKqTWX0+Dvvk8ay4y9k/NO+pyMjAxYWVmxf7SYmJh0mqfW3nKMrEzx7m2HDx/G4cOHkZCQACMjIyxZsgQ7duzAvXv3cObMGWzbtg2enp4CmWzd2WrfHoZh8PDhQ5SVlcHc3BwcDgfa2toYO3YsOy+yqKgI2dnZGDJkCPs5W3sbhv7++2988cUX2LVrl1QLGQCRE6k1NTXR0tKCp0+fCi1mWlpaArt8a2trxW4WJ9JDy4wEQNulFQUFBSgpKeHFixciH0PLMaJzcXFBUlKSwExNRUVF8Hg8/Prrr3jw4AFSUlLA5XKxe/dujB49Gs7OzoiIiEBlZaVIn2cKwzAMcnNzUVpayhayd6mqqmLMmDGYNGkSJk+eDG1tbZSWliIpKQlpaWnIzs7Gw4cPAbzdvOLs7IyAgACsXr26TwwMBt4O/o6MjGS/TktLg6KiIvT19YUeZ2Fhgdu3b7Nf379/HyNHjpTYdZKeQcWMAHj7mc77f3F/8MEHQpcH3j+ms9eT/xs8eLDQ/C4FBQV88skn2LJlCzIzM3H//n1YW1sjNDQUhoaGWLhwIY4ePcrObewKhmGQl5eHkpIS8Hi8Tj9CUFFRgYGBASwsLDB16lQMHz4ciYmJ4PF44HK5WLx4Mby8vODl5dVnChkAcLlcbNy4ETdv3sT169exZs0auLm5se+3o81SDg4OSE5ORkJCApqbmxEYGAhbW1tpXz7pIipmBEDbpRWg8+UVWo6RDgUFBRgZGcHPzw937twBn8/H7Nmzcfz4cYwfPx7z589HSEgISkpKRCpseXl5KC4uhrm5eZcHTQ8aNAj6+vrw9PTEhQsXoKqqCm1tbezatQtcLhdbtmwRqSlZGlxdXeHs7IyFCxfCzc0Nc+bMwd69e9nvd7RZqvX92NraQk9PD1lZWdi0aZM0L52IgTaAEADA9evX4eHhwS4dFRQUwMjICHV1dR1OsKActt7VmsnWGjaakpICS0tLODg4CGSyvSsvLw9FRUXg8Xjd2lzC5/Mxd+5ceHt7w8/PDzU1NYiNjcXZs2cxb948rF69urtvr9eJMvibiIaaponUNDc3Y8SIEQgMDISrqys8PT1RXFyMmJiYXs1howw20bRmsrWGjSYnJ8PU1JQNGx0zZgx8fX2hqKiIDRs2dKuQPXjwgC1YW7du7VNLi6RvomJGpCo6OhpLly7F4MGD8ebNGyQmJsLY2LhXc9gog63rGIZBWVkZoqOjERUVhRs3bmDcuHEoKirC77//DkdHR7ELUG5uLubOnYtly5Zh+/btEo3AIfKDihmRuuLiYqSnp8Pa2hrDhg0T6RhJ5bBRBlv3MQwDf39/BAYGwsrKCklJSRg/frxAJpuoha2goABz586Fk5MTgoODpVbIwsPDsXLlyjbPHzt2DG5ubkKPpTv7voGKGZFbouSwUQZb9wUFBeGXX37BtWvXwOVyUV1djQsXLiAqKgpXrlyBvr4+m8lmYmLSYYF68uQJbG1tMW/ePBw4cECqd2RNTU0C/xnW1dXB1NQUKSkpMDQ0FHos3dn3DTSbkcilpqYmBAYGtpkN+b6cnBzweDxcvnwZ6enpKCgogK+vr5SuUj7U1NTg6tWrMDU1ZUdZubq6Ijo6GmVlZfD390d+fj7mzJkDExMT+Pr6Ii0tDS0tLew5nj59Cjs7O8ycORP79++X+tLiwIEDBcZURURE4PPPP++0kBUVFYFhGHz88cfssVTI5BfdmRGpEzeHjTLYJKe+vl4gk01DQwMODg6YNm0aNm3ahEmTJuHYsWNdymaThMbGRhgYGCAlJQWjR48W+lq6s+876M6MyJ2rV68iJCQEJ0+e7HKgqKamJp49eyb0czYiHlVVVSxatAgnT55EaWkp9u/fj7q6OixfvhwcDgdHjx6VeCHraGDwu+GaJ0+ehJWVVaeFDKA7+/6G7syI1HQ1h40y2HpfeXk5u8wnaaIMDLa0tIS/vz/mzZvX5fPTnX3voUHDRG60l8MGvL0jqK2tbbePrTWDbffu3aioqGg3g41Ilo6OjtR+VmcDg3Nzc5Gbm4tZs2aJdf537+wpXV3+0DIjkQphOWziZrC1Z82aNVBQUGAfwuYftqKAUdkQGRmJBQsWiLw87ezsLDAwOC0tDcOHD6dCJqfozoxIhaOjY4dzAwsKCtp9XllZGUeOHMGRI0dE/jl37tzBxYsXYW1tDQCdfs7TGjC6fv16LFmyBC4uLjA1NcX06dNF/plEOuLj49vtN+toQg3d2fcv9JkZkRvNzc3Q0tJCSUmJyOOaKGBUNjQ0NEBTUxMZGRmYMGGCwPc6mlDz+vVreHp64vTp09DR0YGrqyt8fX0xYAD9DS9t1DRNSBfcvXsX06ZNg66uLoqLizFt2jSEhobiww8/7PCYlStXQkVFBQcPHgTwtqdq5syZnQaTEkJER1vzCemC7OxsGBsb49SpU+Dz+VBWVoaHh4fQYyhglBD5QPfbRG4sW7ZMYMv//v37YWhoiJqamg5nRlLAKCHyge7M+pmnT59CQ0OD3eW1ZcsWTJ48uctpxbJAU1MTLS0tQvvSKGCUEPlAxayf0dPTw88//4wff/wRFRUVCA4OxoEDB+Qik+q7775DZGQk+3VaWhoUFRWhr6/f4TEWFhYC27fv37+PkSNHSvQ6CSE9j4pZP+Tt7Y3nz5/Dzs4Oy5cvB5fL7e1L6hFcLhcbN27EzZs3cf36daxZswZubm7gcDioqanB69ev2xzj4OCA5ORkJCQkoLm5GYGBgbC1tRX6c8LDwwV62Vof4eHhQo+zt7cXeL24zb+EkLaomPVDAwYMwKpVq5CWlsbmi8kDV1dXODs7Y+HChXBzc8OcOXOwd+9eAOiwMVtbWxu7du2Cra0t9PT0kJWVhU2bNgn9OUuXLsWLFy/Yx5MnT6CtrQ0bGxuhx925cwf//vsve9z58+fFf7My5vnz5xgzZkybnsKsrCxYWFhgyJAh8PHxEXm5mxrdyftoa34/VFtbCyMjIxgbG0NNTQ1nz57t7UvqdaIEjHYkICAAhYWFOHToUIev6c9Bo8+ePYO9vT1u376N/Px8dkjwq1evMGHCBNja2sLHxwfe3t5wdnZutzH6XRUVFRg3bpxAo3tgYCA1uvdhtDWfSISvry+sra1x9uxZ3L59WyCJt78aN24c7O3tu1zIGhsbsWfPnk7HbKWmpuLNmzcYNWoUVFVV4eLighcvXnTnkmWGi4sLXFxc2jwfFxeH6upqBAUFYezYsQgICBBp2suJEyegp6cHPz8/jB8/Hps3b+7SlBgin6iY9TOpqak4duwYdu7cCTU1NezYsQPffPMN6uvre/vSZJKokST9OY4kNDQU3377bZvnMzIyYGVlxa76mJiYiNSsnpGRgRkzZrCbliwtLXH37t2evWgic6iY9TOWlpaoq6uDgYEBgLe9WQUFBZTAK6aQkBCRPnf86aefEBcXB2NjYxgZGWH79u04c+aMFK5QOoRlkXWUCP1+w7qCggKUlJQ6vWOlRnfSHmqaJkRM3Ykkkbc4kkOHDnWYRdaR9xvWgf83rQtLg6ZGd9IeKmaEiKkrkSTvB43KWxxJZ1lk7dHS0kJWVpbAc6I0rVOjO2kPLTMSIqb4+Pg2O+g66mdrjSNJSUlBbGwsxZGgbcN6QUEBXr16JfRurr3jqNGdAFTMCBFLQ0MDUlJS8Omnnwo83xNBo+31ZMljP5aNjQ2qq6sREREBAPjtt98wa9YsNoOuJxvdST9QX1/PiPIghEheRUUFY2VlxQBg8vPzGYZhmMbGRmb06NGMh4cHk5uby8yfP585evRop+cqLy9n1NXVGX9/fyYnJ4cxMzNjrl+/LuF30LF331Orc+fOMSoqKoyOjg4zdOhQJisri/2egYEBc+7cuXbPdeDAAUZZWZnR1tZmDAwMmNLSUgleOekuUetMdx7UNE1IHzJr1izY29tj7dq1bINxdHQ03N3dUVRUBA6Hg4yMDHh5eSE5OVnouWQleLS4uBjp6emwtrbGsGHDRD6uO43uRLoonJOQfubRo0cwNDSEgoICW8z8/f2RkpKCS5cuAQAYhsHQoUNRWVkp9FwUPEr6CpoAQkg/015PFvVjEdI5KmaE9HHC+rG6chz1YxF5JnKfGf0SECJdDQ0NePnyJdTU1MDn8wV+B2tra9Hc3Cz091JdXR0lJSXsa6qqqjBw4ED6XSZyie7MCOnjeDwe0tLS2K8LCwtF6scyMzNDamoq+3VmZiZGjBghseskpDdRMSOkj5syZQqqq6tx4sQJAMCuXbswffr0Tvux7OzscOvWLSQmJqK5uRl79uyhQFAit0TezUgIkR5VVVXw+Xx2IHRMTAxWrlwJNTU1tLS0ID4+HhMnTgQAGBkZYceOHbC3t29zntDQUPzwww/Q0NAAh8PBjRs3xBo9RUhfR8WMEBlRUlKCu3fvYtKkSV3qx8rLy8N///2HKVOmUD8WkVtUzAghhMg8+syMEEKIzKNiRgghROZRMSOEECLzqJgRQgiReVTMCCGEyDwqZoQQQmQeFTNCCCEyj4oZIYQQmUfFjBBCiMz7H/VllRlQ8R5UAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 400x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import matplotlib as mlp\n",
    "import numpy as np\n",
    "import math\n",
    "import warnings\n",
    "\n",
    "%matplotlib inline\n",
    "plt.rcParams[\"font.sans-serif\"] = \"SimHei\"\n",
    "plt.rcParams[\"axes.unicode_minus\"] = False\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "x = np.arange(-10,10,0.1)\n",
    "y = np.arange(-10,10,0.1)\n",
    "xx, yy = np.meshgrid(x,y)\n",
    "\n",
    "zz = np.zeros_like(xx)\n",
    "for idx, vx in enumerate(x):\n",
    "    for idy, vy in enumerate(y):\n",
    "        zz[idx,idy] = math.sqrt(math.pow(vx,2) + math.pow(vy,2))\n",
    "\n",
    "fig = plt.figure(figsize=(4,6),facecolor=\"whitesmoke\", edgecolor=\"gray\")\n",
    "ax = Axes3D(fig)\n",
    "ax.plot_surface(xx,yy,zz,\n",
    "                rstride=1,  # rstride（row）\n",
    "                cstride=1,  # cstride(column)\n",
    "                cmap=plt.cm.autumn) \n",
    "ax.grid(alpha=0.45)\n",
    "ax.set_title(\"$f(x) = \\sqrt{x^2+y^2}$ plot\")\n",
    "ax.set_xlabel(\"x\")\n",
    "ax.set_ylabel(\"y\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8558e8f-3d8b-4744-9ef5-c67d79906eb3",
   "metadata": {},
   "source": [
    "# First-Order Differential Equation\n",
    "## Closed-form Equation\n",
    "$$\n",
    "    \\frac{dy}{dx} + P(x)y = Q(x)\n",
    "$$\n",
    "\n",
    "## Numerical Solution\n",
    "$$\n",
    "    \\frac{dy}{dx} = f(x,y(x))\n",
    "$$\n",
    "transfer equation above into difference equation\n",
    "$$\n",
    "    y_{n+1} = y_n + hf(x_n,y(x_n))\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b201de68-1ea4-458d-9b75-0034e4662757",
   "metadata": {},
   "source": [
    "## Closed-Form\n",
    "python sympy package\n",
    "<hr>\n",
    "dependence variable - <font color=red><b>sym.Function(\"alias\")</b></font> <br>\n",
    "independence variable - <font color=red><b>sym.symbols(\"alias\",positive, negative, real, odd, even)</b> </font> <br>\n",
    "derivative function = <font color=red><b>sym.Eq(left,right)</b></font> <br>\n",
    "solve handle = <font color=red><b>sym.dsolve(eq)</b></font> <br>\n",
    "<hr>\n",
    "sym derivative: <br>\n",
    "    > <font color=red><b>sym.y(x).diff(x,2)</b></font> where y is a sym.Function instance, x is a sym.symbols instance <br>\n",
    "sym.intergration: <br>\n",
    "    > <font color=red><b>sym.integrate(a,b,x) </b></font> <br>\n",
    "sym print <br>\n",
    "    > <font color=red><b>sym.pprint(res) </b></font> <br>\n",
    "    > <font color=red><b>sym.latex(res) </b></font> <br>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37f8bff6-a48c-4893-8525-ec17eadd5460",
   "metadata": {},
   "source": [
    "$$\n",
    "    cos(y)\\frac{dy}{dx} - sin(y) = cos(x){sin}^2(y)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "bb0954bd-1a18-4884-a19e-a253c15467d3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "⎡           ⎛            x        ⎞                 ⎛            x        ⎞⎤\n",
      "⎢           ⎜         2⋅ℯ         ⎟                 ⎜         2⋅ℯ         ⎟⎥\n",
      "⎢y(x) = asin⎜─────────────────────⎟ + π, y(x) = asin⎜─────────────────────⎟⎥\n",
      "⎢           ⎜         x    ⎛    π⎞⎟                 ⎜         x    ⎛    π⎞⎟⎥\n",
      "⎢           ⎜C₁ + √2⋅ℯ ⋅sin⎜x + ─⎟⎟                 ⎜C₁ - √2⋅ℯ ⋅sin⎜x + ─⎟⎟⎥\n",
      "⎣           ⎝              ⎝    4⎠⎠                 ⎝              ⎝    4⎠⎠⎦\n"
     ]
    }
   ],
   "source": [
    "import sympy as sym\n",
    "import numpy as np\n",
    "import math\n",
    "import warnings\n",
    "\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "x = sym.symbols(\"x\")\n",
    "y = sym.Function(\"y\")\n",
    "ode = sym.Eq(sym.cos(y(x))*y(x).diff(x,1) - sym.sin(y(x)) - sym.cos(x) * sym.sin(y(x))**2,0)\n",
    "res = sym.dsolve(ode)\n",
    "# print(sym.latex(res))\n",
    "sym.pprint(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b483edce-a6c4-498a-9128-58ae11eed983",
   "metadata": {},
   "source": [
    "$$\n",
    "    \\left[ y{\\left(x \\right)} = \\operatorname{asin}{\\left(\\frac{2 e^{x}}{C_{1} + \\sqrt{2} e^{x} \\sin{\\left(x + \\frac{\\pi}{4} \\right)}} \\right)} + \\pi, \\  y{\\left(x \\right)} = \\operatorname{asin}{\\left(\\frac{2 e^{x}}{C_{1} - \\sqrt{2} e^{x} \\sin{\\left(x + \\frac{\\pi}{4} \\right)}} \\right)}\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8dba09e0-36f9-41a5-bdd9-eb0825cdb076",
   "metadata": {},
   "source": [
    "### initial value and bounding value\n",
    "1. importing initial or bounding values:\n",
    "   > <font color=maroon><b>{y(value):value}</b></font> <br>\n",
    "2. solve problem\n",
    "   > <font color=maroon><b>sym.dsolve(sym.Eq,ics)</b></font> <br>\n",
    "\n",
    "practice this:\n",
    "$$\n",
    "\\left\\{\n",
    "\\begin{array}{ll}\n",
    "\\frac{dy}{dx} + sinx\\space y & = & 3cosxsinx \\\\\n",
    "y(0) = 3\n",
    "\\end{array}\n",
    "\\right .\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "3e7b412e-0c8e-47bf-b369-3aea974e0c0b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        -1  cos(x)             \n",
      "y(x) = ℯ  ⋅ℯ       + cos(x) + 1\n"
     ]
    }
   ],
   "source": [
    "import sympy as sym\n",
    "import numpy as np\n",
    "import math\n",
    "import warnings\n",
    "\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "x = sym.symbols(\"x\")\n",
    "y = sym.Function(\"y\")\n",
    "ode = sym.Eq(y(x).diff(x,1)+sym.sin(x)*y(x) - sym.cos(x)* sym.sin(x),0)\n",
    "con = {y(0):3}\n",
    "res = sym.dsolve(ode,ics=con)\n",
    "# print(sym.latex(res))\n",
    "sym.pprint(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16734076-d5e0-4004-97d4-a07148ec6471",
   "metadata": {},
   "source": [
    "$$\n",
    "y{\\left(x \\right)} = \\frac{e^{\\cos{\\left(x \\right)}}}{e} + \\cos{\\left(x \\right)} + 1\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "587434fd-a6ed-4d69-82cf-160705de6fea",
   "metadata": {},
   "source": [
    "practice this:\n",
    "$$\n",
    "\\left\\{\n",
    "\\begin{array}{ll}\n",
    "f^{\\prime\\prime}(x) - 2f^{\\prime}(x) + 3f(x) = 4  \\\\\n",
    "f(0) = 16 \\\\\n",
    "f^{\\prime}(0) = 18 \\\\\n",
    "\\end{array}\n",
    "\\right .\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "caa837c0-cf23-4c2e-af88-493f5b5785d2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                      x\n",
      "f(x) = (√2⋅sin(√2⋅x) + 16⋅cos(√2⋅x))⋅ℯ \n"
     ]
    }
   ],
   "source": [
    "import sympy as smy\n",
    "import numpy as np \n",
    "import warnings\n",
    "\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "x = sym.symbols(\"x\")\n",
    "f = sym.Function(\"f\")\n",
    "ode = sym.Eq(f(x).diff(x,2)-2*f(x).diff(x,1)+3*f(x),0)\n",
    "con = {f(0):16,f(x).diff(x,1).subs(x,0):18}\n",
    "res = sym.dsolve(ode,ics=con)\n",
    "# lres = sym.latex(res)\n",
    "# print(lres)\n",
    "sym.pprint(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d3332eaf-8ec5-41da-8fc6-542e64a30679",
   "metadata": {},
   "source": [
    "$$\n",
    "    f{\\left(x \\right)} = \\left(\\sqrt{2} \\sin{\\left(\\sqrt{2} x \\right)} + 16 \\cos{\\left(\\sqrt{2} x \\right)}\\right) e^{x}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "5249c94a-0f1a-4029-9790-3f570ac4f141",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fcb8d8ac4f0>"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib as mpl\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "%matplotlib inline\n",
    "resx = np.linspace(-10,100,1000)\n",
    "cp = np.sqrt(2)\n",
    "resy = (cp*np.sin(cp*resx) + 16*np.cos(cp*resx))*np.exp(resx)\n",
    "fig,ax = plt.subplots(1,1,figsize=(6,4),\n",
    "                     facecolor=\"whitesmoke\",\n",
    "                     edgecolor=\"gray\")\n",
    "ax.plot(resx,resy/10,label=\"function plot\", lw=1.5, ls=\"-\")\n",
    "ax.set_ylabel(r\"$\\frac{y}{10}$\",rotation=45)\n",
    "ax.grid(alpha=0.4)\n",
    "ax.legend(loc=\"best\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09a5076b-a633-4caf-841a-a4a5d43f0d45",
   "metadata": {},
   "source": [
    "### Equation Set\n",
    "1. eq = [sym.Eq, sym.Eq, ...]\n",
    "1. sym.dsolve(eq, ics={}) <br>\n",
    "\n",
    "practice this:\n",
    "$$\n",
    "\\left\\{\n",
    "\\begin{array}{ll}\n",
    "\\frac{dy}{dx} = z + 2e^{x} \\\\\n",
    "\\frac{dz}{dx} = y + e^{x} \\\\\n",
    "y(0) = 2 \\\\\n",
    "z(0) = 4 \\\\\n",
    "\\end{array}\n",
    "\\right .\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "05a35cb3-c5dc-4aea-9bea-60aa45c6b939",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sym\n",
    "import numpy as np\n",
    "import math\n",
    "import warnings\n",
    "\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "x = sym.symbols(\"x\")\n",
    "y,z = sym.symbols(\"y,z\", cls=sym.Function)\n",
    "ode = [sym.Eq(y(x).diff(x,1),z(x)+2*sym.exp(x)), sym.Eq(z(x).diff(x,1),y(x)+sym.exp(x))]\n",
    "con = {y(0):2, z(0):4}\n",
    "res = sym.dsolve(ode,ics=con)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "7f78d931-0a04-4b06-b818-0a0a0fc946ad",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "⎡            x       x      -x              x       x      -x⎤\n",
      "⎢       3⋅x⋅ℯ    13⋅ℯ    5⋅ℯ           3⋅x⋅ℯ    11⋅ℯ    5⋅ℯ  ⎥\n",
      "⎢y(x) = ────── + ───── - ─────, z(x) = ────── + ───── + ─────⎥\n",
      "⎣         2        4       4             2        4       4  ⎦\n"
     ]
    }
   ],
   "source": [
    "sym.pprint(res)\n",
    "#print(sym.latex(res))"
   ]
  },
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   "source": [
    "$$\n",
    "\\left[ y{\\left(x \\right)} = \\frac{3 x e^{x}}{2} + \\frac{13 e^{x}}{4} - \\frac{5 e^{- x}}{4}, \\  z{\\left(x \\right)} = \\frac{3 x e^{x}}{2} + \\frac{11 e^{x}}{4} + \\frac{5 e^{- x}}{4}\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "## numerical solution\n",
    "1. <font color=maroon><b>scipy.integrate</b></font> package\n",
    "2. most commonly used one for initial value problem: <font color=maroon><b>solve_ivp</b></font>\n",
    "3. most commonly used one for boundary value problem: <font color=maroon><b>solve_bvp</b></font> <br>\n",
    "for first-order ODE, which is:\n",
    "\n",
    "$$\n",
    "    \\frac{d\\vec y}{dt} = f(t,\\vec y), \\vec y(t_0) = \\vec y_o\n",
    "$$\n",
    "parameters are:<br>\n",
    "> f: function <br>\n",
    "> scale: (t0,t1) <br>\n",
    "> initial value [y_0] <br>\n",
    "> method: <font color=maroon><b>RK23 RK45</b></font> <br>\n",
    "> dense_output: default False, for plotting purposes <br>"
   ]
  },
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   "cell_type": "markdown",
   "id": "d982d25a-2e16-442b-bb0d-b5c616f5ab12",
   "metadata": {},
   "source": [
    "$$\n",
    "    \\frac{dy}{dt} = sin(3t)\\space y + cos(2t)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "11746cd1-6677-4ffe-917e-a04948d67db5",
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (2347104976.py, line 6)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  Cell \u001b[0;32mIn[19], line 6\u001b[0;36m\u001b[0m\n\u001b[0;31m    func =\u001b[0m\n\u001b[0m           ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
     ]
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   ],
   "source": [
    "import scipy.integrate\n",
    "import numpy as np\n",
    "import warnings\n",
    "\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "func = \n",
    "integrate.solve_ivp()"
   ]
  },
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   "cell_type": "markdown",
   "id": "be5f0195-c6e5-4a38-8176-d7b54bd7ea30",
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   "source": [
    "$$\n",
    "\\begin{eqnarray} y_0 - \\alpha &=& 0 \\ \\frac{y_{i-1} - 2 y_i + y_{i+1}}{h^2} + (3 y_i) (\\frac{y_{i+1} - y_{i-1}}{2 h}) &=& 0 \\ y_L - \\beta &=&0 \\end{eqnarray}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "684fe67f-00b3-4cf8-a93b-159b779db23f",
   "metadata": {},
   "source": [
    "### ivp and bvp difference\n",
    "1. difference function needs at least one initial value $y(0)$ to calculate following numerical values, this initial value problem could just use this initial value as a strating point\n",
    "2. we could use one step R-K method or even Adams linearmulti-step methods.\n",
    "3. but for boundary value problem, we needs more alter of function to suit boundary values."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0020b204-2688-4e61-abfb-20a5efe52f5a",
   "metadata": {},
   "source": [
    "### notice \n",
    "1. notice that solve_ivp and solve_bvp methods could only handle first-order derivative function, thus linear higher-order derivative function should convert to first-order for calculation."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5400ffd8-4aa6-4e9f-a48e-fd77b4b84c30",
   "metadata": {},
   "source": [
    "# Numerical Integration and Numerical Differentiation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "baa9f4a1-bbe3-44a2-8d37-0d53dc21c23f",
   "metadata": {},
   "source": [
    "## Numerical Integration\n",
    "1. Newton -Leibniz Formula\n",
    "\n",
    "$$\n",
    "    \\int_{a}^{b} f(x)dx = F(b) - F(a)\n",
    "$$\n",
    "\n",
    "2. Mean Value Theorem of Integrals\n",
    "\n",
    "$$\n",
    "\\begin{array}{ll}\n",
    "    \\int_{a}^{b} f(x)dx = (b-a)f(\\xi), \\space \\xi \\in (a,b) \\\\\n",
    "    where \\space f(x) \\in C[a,b]\n",
    "\\end{array}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "104550b8-3c19-4164-b1d4-89b61656ed1d",
   "metadata": {},
   "source": [
    "### Basic Theorem\n",
    "$$\n",
    "    \\int_{a}^{b}f(x)dx = \\displaystyle\\sum_{k=0}^{n}A_kf(x_k)\n",
    "$$"
   ]
  },
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   "execution_count": null,
   "id": "c7909c5c-392d-4a4a-bba2-cab90b9b0ce5",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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